{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:48:28Z","timestamp":1757310508474,"version":"3.38.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T00:00:00Z","timestamp":1737676800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T00:00:00Z","timestamp":1737676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biol Cybern"],"DOI":"10.1007\/s00422-025-01004-6","type":"journal-article","created":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T06:01:29Z","timestamp":1737698489000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient stochastic simulation of piecewise-deterministic Markov processes and its application to the Morris\u2013Lecar model of neural dynamics"],"prefix":"10.1007","volume":"119","author":[{"given":"Arkady","family":"Pikovsky","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,24]]},"reference":[{"key":"1004_CR1","doi-asserted-by":"crossref","unstructured":"Alfonsi, A., Cances, E., Turinici, G., Di\u00a0Ventura, B., Huisinga, W.: Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. In: ESAIM: proceedings, vol 14, pp 1\u201313 (2005). EDP Sciences","DOI":"10.1051\/proc:2005001"},{"issue":"21","key":"1004_CR2","doi-asserted-by":"publisher","first-page":"214107","DOI":"10.1063\/1.2799998","volume":"127","author":"DF Anderson","year":"2007","unstructured":"Anderson DF (2007) A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J Chem Phys 127(21):214107","journal-title":"J Chem Phys"},{"key":"1004_CR3","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s10827-014-0528-2","volume":"38","author":"DF Anderson","year":"2015","unstructured":"Anderson DF, Ermentrout B, Thomas PJ (2015) Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics. J Comput Neurosci 38:67\u201382","journal-title":"J Comput Neurosci"},{"issue":"1","key":"1004_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13408-018-0067-7","volume":"8","author":"PC Bressloff","year":"2018","unstructured":"Bressloff PC, Maclaurin JN (2018) Stochastic hybrid systems in cellular neuroscience. J Math Neurosci 8(1):1\u201371","journal-title":"J Math Neurosci"},{"key":"1004_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/9781119121534","volume-title":"Numerical methods for ordinary differential equations","author":"JC Butcher","year":"2016","unstructured":"Butcher JC (2016) Numerical methods for ordinary differential equations. Wiley, Chichester"},{"key":"1004_CR6","doi-asserted-by":"publisher","DOI":"10.1201\/9780203748039","volume-title":"Markov models & optimization","author":"MH Davis","year":"2018","unstructured":"Davis MH (2018) Markov models & optimization. Springer, Dordrecht"},{"issue":"24","key":"1004_CR7","doi-asserted-by":"publisher","first-page":"244107","DOI":"10.1063\/1.4971429","volume":"145","author":"S Ding","year":"2016","unstructured":"Ding S, Qian M, Qian H, Zhang X (2016) Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin\u2013Huxley model. J Chem Phys 145(24):244107","journal-title":"J Chem Phys"},{"issue":"2","key":"1004_CR8","doi-asserted-by":"publisher","first-page":"404","DOI":"10.2307\/1427443","volume":"26","author":"P Embrechts","year":"1994","unstructured":"Embrechts P, Schmidli H (1994) Ruin estimation for a general insurance risk model. Adv Appl Probab 26(2):404\u2013422. https:\/\/doi.org\/10.2307\/1427443","journal-title":"Adv Appl Probab"},{"issue":"25","key":"1004_CR9","doi-asserted-by":"publisher","first-page":"2340","DOI":"10.1021\/j100540a008","volume":"81","author":"DT Gillespie","year":"1977","unstructured":"Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340\u20132361","journal-title":"J Phys Chem"},{"key":"1004_CR10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218339023400028","author":"M Hawker","year":"2024","unstructured":"Hawker M, Siekmann I (2024) \u201cPeople\u2019\u2019 meet \u201cmarkovians\u2019\u2019\u2014individual-based modeling with hybrid stochastic systems. J Biol Syst. https:\/\/doi.org\/10.1142\/S0218339023400028","journal-title":"J Biol Syst"},{"issue":"2\u20133","key":"1004_CR11","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1016\/0167-2789(82)90034-3","volume":"5","author":"M H\u00e9non","year":"1982","unstructured":"H\u00e9non M (1982) On the numerical computation of Poincar\u00e9 maps. Physica D 5(2\u20133):412\u2013414","journal-title":"Physica D"},{"issue":"8","key":"1004_CR12","doi-asserted-by":"publisher","first-page":"1353","DOI":"10.1016\/j.na.2005.01.112","volume":"62","author":"JP Hespanha","year":"2005","unstructured":"Hespanha JP (2005) A model for stochastic hybrid systems with application to communication networks. Nonlinear Anal Theory Methods Appl 62(8):1353\u20131383","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"1004_CR13","volume-title":"Stochastic hybrid systems","author":"JP Hespanha","year":"2018","unstructured":"Hespanha JP, Cassandras CG, Blom HA, Lygeros J, Katoen J-P, Prandini M, Schaft A, Wardi Y, Mosterman PJ (2018) Stochastic hybrid systems. CRC Press"},{"key":"1004_CR14","volume-title":"Ion channels of excitable membranes","author":"B Hille","year":"2001","unstructured":"Hille B (2001) Ion channels of excitable membranes. Sinauer Associates, Sunderland"},{"key":"1004_CR15","volume-title":"Noise-induced transitions: theory and applications in physics, chemistry and biology","author":"W Horsthemke","year":"1984","unstructured":"Horsthemke W, Lefever R (1984) Noise-induced transitions: theory and applications in physics, chemistry and biology. Springer, Berlin"},{"key":"1004_CR16","volume-title":"Point process theory and applications. Marked point and piecewise deterministic processes","author":"M Jacobsen","year":"2006","unstructured":"Jacobsen M (2006) Point process theory and applications. Marked point and piecewise deterministic processes. Birkh\u00e4user, Boston"},{"key":"1004_CR17","unstructured":"K\u00f6rner, A.: Mathematical characterisation of state events in hybrid modelling. PhD thesis, Ph. D. thesis, Technische Universit\u00e4t Wien (2015)"},{"key":"1004_CR18","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.mbs.2018.09.009","volume":"305","author":"P Kurasov","year":"2018","unstructured":"Kurasov P, L\u00fcck A, Mugnolo D, Wolf V (2018) Stochastic hybrid models of gene regulatory networks-a PDE approach. Math Biosci 305:170\u2013177","journal-title":"Math Biosci"},{"key":"1004_CR19","doi-asserted-by":"publisher","first-page":"1776","DOI":"10.1007\/s10915-017-0607-4","volume":"75","author":"V Lemaire","year":"2018","unstructured":"Lemaire V, Thieullen M, Thomas N (2018) Exact simulation of the jump times of a class of piecewise deterministic Markov processes. J Sci Comput 75:1776\u20131807","journal-title":"J Sci Comput"},{"issue":"1","key":"1004_CR20","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1017\/apr.2019.55","volume":"52","author":"V Lemaire","year":"2020","unstructured":"Lemaire V, Thieullen M, Thomas N (2020) Thinning and multilevel Monte Carlo methods for piecewise deterministic Markov processes with an application to a stochastic Morris\u2013Lecar model. Adv Appl Probab 52(1):138\u2013172","journal-title":"Adv Appl Probab"},{"issue":"3","key":"1004_CR21","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1002\/nav.3800260304","volume":"26","author":"PAW Lewis","year":"1979","unstructured":"Lewis PAW, Shedler GS (1979) Simulation of nonhomogeneous Poisson processes by thinning. Nav Res Logist Q 26(3):403\u2013413","journal-title":"Nav Res Logist Q"},{"key":"1004_CR22","first-page":"1","volume":"2017","author":"X Li","year":"2017","unstructured":"Li X, Omotere O, Qian L, Dougherty ER (2017) Review of stochastic hybrid systems with applications in biological systems modeling and analysis. EURASIP J Bioinf Syst Biol 2017:1\u201312","journal-title":"EURASIP J Bioinf Syst Biol"},{"issue":"34","key":"1004_CR23","doi-asserted-by":"publisher","first-page":"12295","DOI":"10.1073\/pnas.0805549105","volume":"105","author":"J Lygeros","year":"2008","unstructured":"Lygeros J, Koutroumpas K, Dimopoulos S, Legouras I, Kouretas P, Heichinger C, Nurse P, Lygerou Z (2008) Stochastic hybrid modeling of DNA replication across a complete genome. Proc Natl Acad Sci 105(34):12295\u201312300","journal-title":"Proc Natl Acad Sci"},{"key":"1004_CR24","doi-asserted-by":"crossref","unstructured":"Masuda, N., Vestergaard, C.L.: Gillespie algorithms for stochastic multiagent dynamics in populations and networks. In: Elements in structure and dynamics of complex networks (2022)","DOI":"10.1017\/9781009239158"},{"issue":"1","key":"1004_CR25","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0006-3495(81)84782-0","volume":"35","author":"C Morris","year":"1981","unstructured":"Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193\u2013213","journal-title":"Biophys J"},{"key":"1004_CR26","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.cam.2012.09.021","volume":"239","author":"MG Riedler","year":"2013","unstructured":"Riedler MG (2013) Almost sure convergence of numerical approximations for piecewise deterministic Markov processes. J Comput Appl Math 239:50\u201371","journal-title":"J Comput Appl Math"},{"key":"1004_CR27","volume-title":"Stochastic modelling for systems biology","author":"DJ Wilkinson","year":"2018","unstructured":"Wilkinson DJ (2018) Stochastic modelling for systems biology. Chapman and Hall\/CRC, Boca Raton"}],"container-title":["Biological Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-025-01004-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00422-025-01004-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00422-025-01004-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T16:50:25Z","timestamp":1740588625000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00422-025-01004-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,24]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["1004"],"URL":"https:\/\/doi.org\/10.1007\/s00422-025-01004-6","relation":{},"ISSN":["1432-0770"],"issn-type":[{"type":"electronic","value":"1432-0770"}],"subject":[],"published":{"date-parts":[[2025,1,24]]},"assertion":[{"value":"4 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"No ethical approval needed.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"No extra consent for publication needed.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"5"}}