{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T12:19:27Z","timestamp":1725538767962},"publisher-location":"Berlin, Heidelberg","reference-count":53,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642041853"},{"type":"electronic","value":"9783642041860"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-04186-0_11","type":"book-chapter","created":{"date-parts":[[2009,10,1]],"date-time":"2009-10-01T16:07:04Z","timestamp":1254413224000},"page":"216-267","source":"Crossref","is-referenced-by-count":11,"title":["Dynamical Systems and Stochastic Programming: To Ordinary Differential Equations and Back"],"prefix":"10.1007","author":[{"given":"Luca","family":"Bortolussi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alberto","family":"Policriti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"11_CR1","unstructured":"Converging sciences. Trento (2004), http:\/\/www.unitn.it\/events\/consci\/"},{"key":"11_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-45351-2_6","volume-title":"Hybrid Systems: Computation and Control","author":"R. Alur","year":"2001","unstructured":"Alur, R., Belta, C., Ivancic, F., Kumar, V., Mintz, M., Pappas, G., Rubin, H., Schug, J.: Hybrid modeling and simulation of biomolecular networks. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol.\u00a02034, pp. 19\u201332. Springer, Heidelberg (2001)"},{"issue":"3","key":"11_CR3","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1385\/CBB:38:3:271","volume":"38","author":"M. Antoniotti","year":"2003","unstructured":"Antoniotti, M., Policriti, A., Ugel, N., Mishra, B.: Model building and model checking for biochemical processes. Cell Biochemistry and Biophysics\u00a038(3), 271\u2013286 (2003)","journal-title":"Cell Biochemistry and Biophysics"},{"key":"11_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61474-5_75","volume-title":"Computer Aided Verification","author":"A. Aziz","year":"1996","unstructured":"Aziz, A., Singhal, V., Balarin, F., Brayton, R., Sangiovanni-Vincentelli, A.: Verifying continuous time markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol.\u00a01102. Springer, Heidelberg (1996)"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Blossey, R., Cardelli, L., Phillips, A.: A compositional approach to the stochastic dynamics of gene networks. T. Comp. Sys. Biology, 99\u2013122 (2006)","DOI":"10.1007\/11732488_10"},{"key":"11_CR6","doi-asserted-by":"crossref","unstructured":"Blossey, R., Cardelli, L., Phillips, A.: Compositionality, stochasticity and cooperativity in dynamic models of gene regulation. HFPS Journal (2007) (in print)","DOI":"10.2976\/1.2804749"},{"key":"11_CR7","doi-asserted-by":"crossref","unstructured":"Bortolussi, L.: Stochastic concurrent constraint programming. In: Proceedings of 4th International Workshop on Quantitative Aspects of Programming Languages (QAPL 2006). ENTCS, vol.\u00a0164, pp. 65\u201380 (2006)","DOI":"10.1016\/j.entcs.2006.07.012"},{"key":"11_CR8","unstructured":"Bortolussi, L.: Constraint-based approaches to stochastic dynamics of biological systems. PhD thesis, PhD in Computer Science, University of Udine (2007), http:\/\/www.dmi.units.it\/~bortolu\/files\/reps\/Bortolussi-PhDThesis.pdf"},{"key":"11_CR9","unstructured":"Bortolussi, L.: A master equation approach to differential approximations of stochastic concurrent constraint programming. In: Proceedings of QAPL 2008. ENTCS (2008) (to appear)"},{"key":"11_CR10","doi-asserted-by":"crossref","unstructured":"Bortolussi, L., Fonda, S., Policriti, A.: Constraint-based simulation of biological systems described by molecular interaction maps. In: Proceedings of IEEE conference on Bioinformatics and Biomedicine, BIBM 2007 (2007)","DOI":"10.1109\/BIBM.2007.31"},{"key":"11_CR11","unstructured":"Bortolussi, L., Policriti, A.: Relating stochastic process algebras and differential equations for biological modeling. In: Proceedings of PASTA 2006 (2006)"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"Bortolussi, L., Policriti, A.: Stochastic concurrent constraint programming and differential equations. In: Proceedings of Fifth Workshop on Quantitative Aspects of Programming Languages, QAPL 2007. ENTCS, vol.\u00a016713 (2007)","DOI":"10.1016\/j.entcs.2007.07.003"},{"key":"11_CR13","unstructured":"Bortolussi, L., Policriti, A.: Hybrid approximation of stochastic concurrent constraint programming. In: Proceedings of IFAC 2008 (2008)"},{"key":"11_CR14","unstructured":"Bortolussi, L., Policriti, A.: The importance of being (a little bit) discrete. In: Proceedings of FBTC 2008. ENTCS (2008) (to appear)"},{"key":"11_CR15","doi-asserted-by":"crossref","unstructured":"Bortolussi, L., Policriti, A.: Modeling biological systems in concurrent constraint programming. Constraints\u00a013(1) (2008)","DOI":"10.1007\/s10601-007-9034-8"},{"key":"11_CR16","unstructured":"Cardelli, L.: From processes to odes by chemistry (2006), http:\/\/lucacardelli.name\/"},{"issue":"3","key":"11_CR17","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.tcs.2007.11.012","volume":"391","author":"L. Cardelli","year":"2008","unstructured":"Cardelli, L.: On process rate semantics. Theoretical Computer Science\u00a0391(3), 190\u2013215 (2008)","journal-title":"Theoretical Computer Science"},{"key":"11_CR18","unstructured":"Ciocchetta, F., Hillston, J.: Bio-PEPA: an extension of the process algebra PEPA for biochemical networks. In: Proceeding of FBTC 2007. Workshop of CONCUR 2007 (2007)"},{"key":"11_CR19","unstructured":"Seattle CompBio Group, Institute for Systems Biology. Dizzy home page"},{"key":"11_CR20","unstructured":"Cornish-Bowden, A.: Fundamentals of Chemical Kinetics, 3rd edn. Portland Press (2004)"},{"key":"11_CR21","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1038\/35002125","volume":"403","author":"M.B. Elowitz","year":"2000","unstructured":"Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature\u00a0403, 335\u2013338 (2000)","journal-title":"Nature"},{"key":"11_CR22","doi-asserted-by":"crossref","unstructured":"Geisweiller, N., Hillston, J., Stenico, M.: Relating continuous and discrete pepa models of signalling pathways. Theoretical Computer Science (2008) (in print)","DOI":"10.1016\/j.tcs.2008.04.012"},{"issue":"1","key":"11_CR23","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1063\/1.481811","volume":"113","author":"D. Gillespie","year":"2000","unstructured":"Gillespie, D.: The chemical langevin equation. Journal of Chemical Physics\u00a0113(1), 297\u2013306 (2000)","journal-title":"Journal of Chemical Physics"},{"key":"11_CR24","volume-title":"System Modelling in Cellular Biology","author":"D. Gillespie","year":"2006","unstructured":"Gillespie, D., Petzold, L.: Numerical Simulation for Biochemical Kinetics. In: System Modelling in Cellular Biology. MIT Press, Cambridge (2006)"},{"key":"11_CR25","doi-asserted-by":"crossref","unstructured":"Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. of Computational Physics\u00a022 (1976)","DOI":"10.1016\/0021-9991(76)90041-3"},{"key":"11_CR26","doi-asserted-by":"crossref","unstructured":"Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. of Physical Chemistry\u00a081(25) (1977)","DOI":"10.1021\/j100540a008"},{"key":"11_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/b97265","volume-title":"Stochastic Petri Nets","author":"P.J. Haas","year":"2002","unstructured":"Haas, P.J.: Stochastic Petri Nets. Springer, Heidelberg (2002)"},{"issue":"3","key":"11_CR28","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1137\/0128057","volume":"28","author":"S.P. Hastings","year":"1975","unstructured":"Hastings, S.P., Murray, J.D.: The existence of oscillatory solutions in the field-noyes model for the belousov-zhabotinskii reaction. SIAM Journal on Applied Mathematics\u00a028(3), 678\u2013688 (1975)","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"11_CR29","doi-asserted-by":"crossref","unstructured":"Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (1996)","DOI":"10.1109\/LICS.1996.561342"},{"key":"11_CR30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569951","volume-title":"A Compositional Approach to Performance Modelling","author":"J. Hillston","year":"1996","unstructured":"Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)"},{"key":"11_CR31","doi-asserted-by":"crossref","unstructured":"Hillston, J.: Fluid flow approximation of PEPA models. In: Proceedings of the Second International Conference on the Quantitative Evaluation of Systems, QEST 2005 (2005)","DOI":"10.1109\/QEST.2005.12"},{"key":"11_CR32","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3087.001.0001","volume-title":"Foundations of Systems Biology","author":"H. Kitano","year":"2001","unstructured":"Kitano, H.: Foundations of Systems Biology. MIT Press, Cambridge (2001)"},{"key":"11_CR33","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1038\/nature01254","volume":"420","author":"H. Kitano","year":"2002","unstructured":"Kitano, H.: Computational systems biology. Nature\u00a0420, 206\u2013210 (2002)","journal-title":"Nature"},{"issue":"1","key":"11_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1091\/mbc.E05-09-0824","volume":"17","author":"K.W. Kohn","year":"2006","unstructured":"Kohn, K.W., Aladjem, M.I., Weinstein, J.N., Pommier, Y.: Molecular interaction maps of bioregulatory networks: A general rubric for systems biology. Molecular Biology of the Cell\u00a017(1), 1\u201313 (2006)","journal-title":"Molecular Biology of the Cell"},{"key":"11_CR35","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1017\/S0021900200026929","volume":"7","author":"T.G. Kurtz","year":"1970","unstructured":"Kurtz, T.G.: Solutions of ordinary differential equations as limits of pure jump markov processes. Journal of Applied Probability\u00a07, 49\u201358 (1970)","journal-title":"Journal of Applied Probability"},{"key":"11_CR36","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1017\/S002190020003535X","volume":"8","author":"T.G. Kurtz","year":"1971","unstructured":"Kurtz, T.G.: Limit theorems for sequences of jump markov processes approximating ordinary differential processes. Journal of Applied Probability\u00a08, 244\u2013356 (1971)","journal-title":"Journal of Applied Probability"},{"issue":"2","key":"11_CR37","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1007\/s10009-004-0140-2","volume":"6","author":"M. Kwiatkowska","year":"2004","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with prism: A hybrid approach. International Journal on Software Tools for Technology Transfer\u00a06(2), 128\u2013142 (2004)","journal-title":"International Journal on Software Tools for Technology Transfer"},{"key":"11_CR38","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1073\/pnas.94.3.814","volume":"94","author":"H.H. Mcadams","year":"1997","unstructured":"Mcadams, H.H., Arkin, A.: Stochastic mechanisms in gene expression. PNAS\u00a094, 814\u2013819 (1997)","journal-title":"PNAS"},{"key":"11_CR39","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810633","volume-title":"Markov Chains","author":"J.R. Norris","year":"1997","unstructured":"Norris, J.R.: Markov Chains. Cambridge University Press, Cambridge (1997)"},{"key":"11_CR40","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1146\/annurev.pc.25.100174.000523","volume":"25","author":"R.M. Noyes","year":"1974","unstructured":"Noyes, R.M., Field, R.J.: Oscillatory chemical reactions. Annual Review of Physical Chemistry\u00a025, 95\u2013119 (1974)","journal-title":"Annual Review of Physical Chemistry"},{"key":"11_CR41","unstructured":"Nurse, P.: Understanding cells. Nature\u00a024 (2003)"},{"key":"11_CR42","doi-asserted-by":"crossref","unstructured":"Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algebr. Program., 60-61, 17\u2013139 (2004)","DOI":"10.1016\/j.jlap.2004.03.009"},{"key":"11_CR43","volume-title":"Numerical Recipes in C++ : The Art of Scientific Computing","author":"W.H. Press","year":"2002","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press, Cambridge (2002)"},{"issue":"6","key":"11_CR44","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1093\/comjnl\/38.7.578","volume":"38","author":"C. Priami","year":"1995","unstructured":"Priami, C.: Stochastic \u03c0-calculus. The Computer Journal\u00a038(6), 578\u2013589 (1995)","journal-title":"The Computer Journal"},{"issue":"1","key":"11_CR45","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/S0020-0190(01)00214-9","volume":"80","author":"C. Priami","year":"2001","unstructured":"Priami, C., Regev, A., Shapiro, E.Y., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inf. Process. Lett.\u00a080(1), 25\u201331 (2001)","journal-title":"Inf. Process. Lett."},{"issue":"2","key":"11_CR46","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1142\/S0219720005001132","volume":"3","author":"S. Ramsey","year":"2005","unstructured":"Ramsey, S., Orrell, D., Bolouri, H.: Dizzy: stochastic simulation of large-scale genetic regulatory networks. Journal of Bioinformatics and Computational Biology\u00a03(2), 415\u2013436 (2005)","journal-title":"Journal of Bioinformatics and Computational Biology"},{"issue":"11","key":"11_CR47","doi-asserted-by":"publisher","first-page":"4999","DOI":"10.1063\/1.1545446","volume":"118","author":"C.V. Rao","year":"2003","unstructured":"Rao, C.V., Arkin, A.P.: Stochastic chemical kinetics and the quasi-steady state assumption: Application to the gillespie algorithm. Journal of Chemical Physics\u00a0118(11), 4999\u20135010 (2003)","journal-title":"Journal of Chemical Physics"},{"key":"11_CR48","doi-asserted-by":"crossref","unstructured":"Regev, A., Shapiro, E.: Cellular abstractions: Cells as computation. Nature\u00a0419 (2002)","DOI":"10.1038\/419343a"},{"key":"11_CR49","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2086.001.0001","volume-title":"Concurrent Constraint Programming","author":"V.A. Saraswat","year":"1993","unstructured":"Saraswat, V.A.: Concurrent Constraint Programming. MIT press, Cambridge (1993)"},{"issue":"5","key":"11_CR50","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1093\/bioinformatics\/btg042","volume":"19","author":"B.E. Shapiro","year":"2003","unstructured":"Shapiro, B.E., Levchenko, A., Meyerowitz, E.M., Wold, B.J., Mjolsness, E.D.: Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations. Bioinformatics\u00a019(5), 677\u2013678 (2003)","journal-title":"Bioinformatics"},{"key":"11_CR51","volume-title":"Non-Linear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry and Engeneering","author":"S.H. Strogatz","year":"1994","unstructured":"Strogatz, S.H.: Non-Linear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry and Engeneering. Perseus books, Cambridge (1994)"},{"issue":"9","key":"11_CR52","doi-asserted-by":"publisher","first-page":"5991","DOI":"10.1073\/pnas.092133899","volume":"99","author":"J.M.G. Vilar","year":"2002","unstructured":"Vilar, J.M.G., Yuan Kueh, H., Barkai, N., Leibler, S.: Mechanisms of noise resistance in genetic oscillators. PNAS\u00a099(9), 5991 (2002)","journal-title":"PNAS"},{"key":"11_CR53","doi-asserted-by":"crossref","DOI":"10.1201\/9781420010664","volume-title":"Stochastic Modelling for Systems Biology","author":"D.J. Wilkinson","year":"2006","unstructured":"Wilkinson, D.J.: Stochastic Modelling for Systems Biology. Chapman & Hall, Boca Raton (2006)"}],"container-title":["Lecture Notes in Computer Science","Transactions on Computational Systems Biology XI"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-04186-0_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T18:06:04Z","timestamp":1633975564000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-04186-0_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642041853","9783642041860"],"references-count":53,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-04186-0_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}