Gillespie Algorithm - Further Reading

Further Reading

  • Gillespie, Daniel T. (1977). "Exact Stochastic Simulation of Coupled Chemical Reactions". The Journal of Physical Chemistry 81 (25): 2340–2361. doi:10.1021/j100540a008.
  • Gillespie, Daniel T. (1976). "A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions". Journal of Computational Physics 22 (4): 403–434. doi:10.1016/0021-9991(76)90041-3.
  • Doob, Jacob L. (1942). "Topics in the Theory of Markoff Chains". Transactions of the American Mathematical Society 52 (1): 37–64. doi:10.1090/S0002-9947-1942-0006633-7. JSTOR 1990152.
  • Doob, Jacob L. (1945). "Markoff chains – Denumerable case". Transactions of the American Mathematical Society 58 (3): 455–473. doi:10.2307/1990339. JSTOR 1990339.
  • Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007). "Section 17.7. Stochastic Simulation of Chemical Reaction Networks". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York, NY: Cambridge University Press. ISBN 978-0-521-88068-8. http://apps.nrbook.com/empanel/index.html#pg=946.
  • Kolmogorov, Andrey N. (1931). "Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung ". Mathematische Annalen 104: 415. doi:10.1007/BF01457949. http://www.springerlink.com/content/v724507673277262/fulltext.pdf.
  • Feller, Willy (1940). "On the Integro-Differential Equations of Purely Discontinous Markoff Processes". Transactions of the American Mathematical Society 48 (3): 4885–15. JSTOR 1970064.
  • Kendall, David G. (1950). "An Artificial Realization of a Simple "Birth-and-Death" Process". Journal of the Royal Statistical Society. Series B (Methodological) 12 (1): 116–119. JSTOR 2983837.
  • Bartlett, Maurice S. (1953). "Stochastic Processes or the Statistics of Change". Journal of the Royal Statistical Society. Series C (Applied Statistics) 2 (1): 44–64. JSTOR 2985327.
  • Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang; and Gillespie, Daniel T. (2003). "Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method". Journal of Chemical Physics 119 (24): 12784–12794. doi:10.1063/1.1627296.
  • Sinitsyn, Nikolai A.; Hengartner, Nicolas; Nemenman, Ilya (2009). "Adiabatic coarse-graining and simulations of stochastic biochemical networks". Proceedings of the National Academy of Sciences of the United States of America 106 (20): 10546–10551. doi:10.1073/pnas.0809340106. PMC 2705573. PMID 19525397. http://www.menem.com/~ilya/wiki/images/1/18/Sinitsyn-etal-09.pdf.
  • Gibson, Michael A.; and Bruck, Jehoshua (2000). "Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels". Journal of Physical Chemistry A 104 (9): 1876–1889. doi:10.1021/jp993732q. http://www.cs.caltech.edu/courses/cs191/paperscs191/JPhysChemA(2000-104)1876.pdf.
  • Salis, Howard; Kaznessis, Yiannis N. (2005). "Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions". Journal of Chemical Physics 122 (5): 054103. doi:10.1063/1.1835951. PMID 15740306.
  • (Slepoy Thompson Plimpton 2008): Slepoy, Alexander; Thompson, Aidan P.; Plimpton, Steven J. (2008). "A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks". Journal of Chemical Physics 128 (20): 205101. doi:10.1063/1.2919546. PMID 18513044.
  • (Bratsun et al. 2005): Bratsun, Dmitri; Volfson, Dmitri; Hasty, Jeff; and Tsimring, Lev S. (2005). "Delay-induced stochastic oscillations in gene regulation". Proceedings of the National Academy of Sciences of the United States of America 102 (41): 14593–8. doi:10.1073/pnas.0503858102. PMC 1253555. PMID 16199522. //www.ncbi.nlm.nih.gov/pmc/articles/PMC1253555/.
  • (Barrio et al. 2006): Barrio, Manuel; Burrage, Kevin; Leier, André; and Tian, Tianhai (2006). "Oscillatory Regulation of hes1: Discrete Stochastic Delay Modelling and Simulation". Public Library of Science (PLoS) Computational Biology 2 (9): 1017. doi:10.1371/journal.pcbi.0020117. PMC 1560403. PMID 16965175. //www.ncbi.nlm.nih.gov/pmc/articles/PMC1560403/.
  • (Cai 2007): Cai, Xiaodong (2007). "Exact stochastic simulation of coupled chemical reactions with delays". Journal of Chemical Physics 126 (12): 124108. doi:10.1063/1.2710253. PMID 17411109.
  • (Barnes Chu 2010): Barnes, David J.; and Chu, Dominique (2010). Introduction to Modeling for Biosciences. Springer Verlag.
  • (Ramaswamy González-Segredo Sbalzarini 2009): Ramaswamy, Rajesh; González-Segredo, Nélido; and Sbalzarini, Ivo F. (2009). "A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks". Journal of Chemical Physics 130 (24): 244104. doi:10.1063/1.3154624. PMID 19566139.
  • (Ramaswamy Sbalzarini 2010): Ramaswamy, Rajesh; and Sbalzarini, Ivo F. (2010). "A partial-propensity variant of the composition-rejection stochastic simulation algorithm for chemical reaction networks". Journal of Chemical Physics 132 (4): 044102. doi:10.1063/1.3297948. PMID 20113014.
  • (Indurkhya Beal 2010): Indurkhya, Sagar; and Beal, Jacob S. (2005). Isalan, Mark. ed. "Reaction Factoring and Bipartite Update Graphs Accelerate the Gillespie Algorithm for Large-Scale Biochemical Systems". Public Library of Science (PLoS) ONE 5 (1): e8125. doi:10.1371/journal.pone.0008125. PMC 2798956. PMID 20066048. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2798956/.
  • (Ramaswamy Sbalzarini 2011): Ramaswamy, Rajesh; and Sbalzarini, Ivo F. (2011). "A partial-propensity formulation of the stochastic simulation algorithm for chemical reaction networks with delays". Journal of Chemical Physics 134 (1): 014106. doi:10.1063/1.3521496. PMID 21218996.

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