{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T03:44:17Z","timestamp":1772163857831,"version":"3.50.1"},"reference-count":56,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U2230402"],"award-info":[{"award-number":["U2230402"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271020"],"award-info":[{"award-number":["12271020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2025,10,31]]},"DOI":"10.1137\/24m1671566","type":"journal-article","created":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T09:00:28Z","timestamp":1757926828000},"page":"1998-2025","source":"Crossref","is-referenced-by-count":2,"title":["Exact Switching Time Distributions for Autoregulated Gene Expression Models with mRNA and Protein Descriptions"],"prefix":"10.1137","volume":"85","author":[{"given":"Shan","family":"Liu","sequence":"first","affiliation":[{"name":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193 China."},{"name":"These authors contributed equally to this work."}]},{"given":"Bingjie","family":"Wu","sequence":"additional","affiliation":[{"name":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193 China."},{"name":"These authors contributed equally to this work."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3375-4373","authenticated-orcid":true,"given":"Chen","family":"Jia","sequence":"additional","affiliation":[{"name":"Corresponding author. Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193 China."}]}],"member":"351","published-online":{"date-parts":[[2025,9,15]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1038\/nrm2503"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1038\/ng881"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1038\/35014651"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0736140100"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1038\/msb.2013.27"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1126\/science.1178962"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2024.105128"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-2836(02)00994-4"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1063\/1.5009749"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1063\/1.5144578"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.72.051907"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.268105"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.118104"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1063\/1.4736721"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1063\/1.4947202"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.052406"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.062902"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1063\/5.0188455"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1063\/5.0007221"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ceb.2020.08.001"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1093\/emboj\/20.10.2528"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.celrep.2014.12.001"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2006.08.016"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1128\/JB.00390-17"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2017.0804"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-05822-0"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2021.0274"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.isci.2022.105746"},{"key":"ref29","first-page":"021032","volume":"11","author":"Jia C.","year":"2021","journal-title":"Phys. Rev. X"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.112318199"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.plrev.2005.03.003"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-017-1196-4"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1063\/1.2145882"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0803850105"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1038\/nature10098"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1400049111"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1137\/23M1560914"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1126\/science.1202142"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2012.06.025"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-023-01913-9"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2024.04.004"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2016.11.001"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-15464-9"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1515\/ijnsns-2019-0258"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-023-01924-6"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2005.09.031"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1038\/nature14562"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1126\/science.1198817"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1804060115"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2018.0967"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1012118"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511790492"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1969.10500983"},{"key":"ref56","first-page":"89","volume":"4","author":"Kolmogorov A.","year":"1933","journal-title":"Giorn. Dell\u2019Inst. Ital. Degli Att."},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-50716-z"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1910888117"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T09:00:30Z","timestamp":1757926830000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1671566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,15]]},"references-count":56,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10,31]]}},"alternative-id":["10.1137\/24M1671566"],"URL":"https:\/\/doi.org\/10.1137\/24m1671566","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.06.24.600551","asserted-by":"object"}]},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,15]]}}}