Hybrid discrete/continuum algorithms for stochastic reaction networks
Tài liệu tham khảo
Gillespie, 1992, A rigorous derivation of the chemical master equation, Physica A, 188, 404, 10.1016/0378-4371(92)90283-V
Gillespie, 1976, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22, 403, 10.1016/0021-9991(76)90041-3
Gillespie, 1977, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 2340, 10.1021/j100540a008
Gibson, 2000, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A, 104, 1876, 10.1021/jp993732q
Rathinam, 2003, Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method, J. Chem. Phys., 119, 12784, 10.1063/1.1627296
Gillespie, 2001, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115, 1716, 10.1063/1.1378322
Haseltine, 2002, Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics, J. Chem. Phys., 117, 6959, 10.1063/1.1505860
Cao, 2004, The numerical stability of leaping methods for stochastic simulation of chemically reacting systems, J. Chem. Phys., 121, 12169, 10.1063/1.1823412
Cao, 2005, The slow-scale stochastic simulation algorithm, J. Chem. Phys., 122, 014116, 10.1063/1.1824902
Cao, 2005, Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems, J. Comput. Phys., 206, 395, 10.1016/j.jcp.2004.12.014
E, 2007, Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales, J. Comput. Phys., 221, 158, 10.1016/j.jcp.2006.06.019
Sandu, 2014, A new look at the chemical master equation, Numer. Algorithms, 65, 485, 10.1007/s11075-013-9758-z
Munsky, 2006, The finite state projection algorithm for the solution of the chemical master equation, J. Chem. Phys., 124, 10.1063/1.2145882
Munsky, 2007, A multiple time interval finite state projection algorithm for the solution to the chemical master equation, J. Comput. Phys., 226, 818, 10.1016/j.jcp.2007.05.016
Munsky, 2008, The finite state projection approach for the analysis of stochastic noise in gene networks, IEEE Trans. Autom. Control, 53, 201, 10.1109/TAC.2007.911361
Sunkara, 2010, An optimal finite state projection method, Proc. Comput. Sci., 1, 1579, 10.1016/j.procs.2010.04.177
Hegland, 2007, A solver for the stochastic master equation applied to gene regulatory networks, J. Comput. Appl. Math., 205, 708, 10.1016/j.cam.2006.02.053
MacNamara, 2008, Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation, J. Chem. Phys., 129, 95, 10.1063/1.2971036
MacNamara, 2008, Multiscale modeling of chemical kinetics via the master equation, Multiscale Model. Simul., 6, 1146, 10.1137/060678154
Sidje, 2007, Inexact uniformization method for computing transient distributions of Markov chains, SIAM J. Sci. Comput., 29, 2562, 10.1137/060662629
Zhang, 2010, A modified uniformization method for the solution of the chemical master equation, Comput. Math. Appl., 59, 573, 10.1016/j.camwa.2009.04.021
Peles, 2006, Reduction and solution of the chemical master equation using time scale separation and finite state projection, J. Chem. Phys., 125, 10.1063/1.2397685
Deuflhard, 2008, Adaptive discrete Galerkin methods applied to the chemical master equation, SIAM J. Sci. Comput., 30, 2990, 10.1137/070689759
Engblom, 2006
Engblom, 2009, Spectral approximation of solutions to the chemical master equation, J. Comput. Appl. Math., 229, 208, 10.1016/j.cam.2008.10.029
Zhang, 2010, Radial basis function collocation for the chemical master equation, Int. J. Comput. Methods, 07, 477, 10.1142/S0219876210002234
Jahnke, 2010, Solving chemical master equations by adaptive wavelet compression, J. Comput. Phys., 229, 5724, 10.1016/j.jcp.2010.04.015
Khanin, 2008, Chemical master equation and Langevin regimes for a gene transcription model, Theor. Comput. Sci., 408, 31, 10.1016/j.tcs.2008.07.007
Gardiner, 2004, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, vol. 13
Sjöberg, 2009, Fokker–Planck approximation of the master equation in molecular biology, Comput. Vis. Sci., 12, 37, 10.1007/s00791-006-0045-6
Sjöberg, 2007
Salis, 2005, Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions, J. Chem. Phys., 122, 10.1063/1.1835951
Haseltine, 2005, On the origins of approximations for stochastic chemical kinetics, J. Chem. Phys., 123, 10.1063/1.2062048
Hellander, 2007, Hybrid method for the chemical master equation, J. Comput. Phys., 227, 100, 10.1016/j.jcp.2007.07.020
Sanft, 2011, Stochkit2: software for discrete stochastic simulation of biochemical systems with events, Bioinformatics, 27, 2457, 10.1093/bioinformatics/btr401
C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Technical Report, ICASE Report No. 97-65; NASA/CR-97-NASA/CR-206253, 1997.
Vilar, 2002, Mechanisms of noise-resistance in genetic oscillators, Proc. Natl. Acad. Sci., 99, 5988, 10.1073/pnas.092133899
Elf, 2003, Near-critical phenomena in intracellular metabolite pools, Biophys. J., 84, 154, 10.1016/S0006-3495(03)74839-5
Ferm, 2004
Scott, 1992
Silverman, 1986
van Kampen, 1992
van Leer, 1979, Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov's method, J. Comput. Phys., 32, 101, 10.1016/0021-9991(79)90145-1
Lax, 1954, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Commun. Pure Appl. Math., 7, 159, 10.1002/cpa.3160070112
LeVeque, 2002
Harten, 1983, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49, 357, 10.1016/0021-9991(83)90136-5
SWIG
Oliphant, 2007, Python for scientific computing, Comput. Sci. Eng., 9, 90, 10.1109/MCSE.2007.58