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Efficient stochastic sampling of first-passage times with applications to self-assembly simulations
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10.1063/1.3026595
/content/aip/journal/jcp/129/20/10.1063/1.3026595
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/20/10.1063/1.3026595
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Illustration of trapped subgraphs in SSA models. (a) A simple CTMM on a three-path with transition rates and . (b) The probability landscape for the model. SSA is slow whenever the invariant density for the corresponding Markov chain is irregular. Here, the SSA takes steps to reach vertex 3. (c) CTMM model of a trimer assembly system with three subunits. Graph of possible configurations joined by reaction rates. States in which the trimer is broken are surrounded by solid lines and others by dashed lines.

Image of FIG. 2.
FIG. 2.

Pseudocode for spectral method 1.

Image of FIG. 3.
FIG. 3.

Schematic of the EMC-based spectral method. Filled vertices are the currently occupied nodes. Simulation advances the system state as a discrete mixture until such time as the state has relaxed to its slowest eigenstate . At each step, direct transitions to the absorbing vertex (gray) are computed according to the Kolmogorov matrix.

Image of FIG. 4.
FIG. 4.

Pseudocode for spectral method 2.

Image of FIG. 5.
FIG. 5.

Pseudocode for AD.

Image of FIG. 6.
FIG. 6.

Number of SSA steps until first passage for the network generated by an -cycle . (a) Average number of steps . (b) Relative deviation .

Image of FIG. 7.
FIG. 7.

Number of SSA steps until first passage on an -dimensional unit hypercube . (a) A plot of the average number of steps vs rate ratio . (b) Relative deviation .

Image of FIG. 8.
FIG. 8.

Number of rejection steps for the master equation method until first passage for the network generated by . (a) Average number of steps . (b) Standard deviation .

Image of FIG. 9.
FIG. 9.

Number of rejection steps for the master equation method until first passage for . (a) Average number of steps . (b) Standard deviation .

Image of FIG. 10.
FIG. 10.

Number of EMC steps until first passage for the network generated by . (a) Average number of steps . (b) Standard deviation . (c) Fraction of times the trajectory escapes before relaxing to the slowest decay mode.

Image of FIG. 11.
FIG. 11.

Number of EMC steps until first passage on . (a) Average number of steps . (b) Standard deviation . (c) Fraction of times the trajectory escapes before relaxing to the slowest decay mode.

Image of FIG. 12.
FIG. 12.

Comparative run times for the network generated by . (a) Ratio of SSA to master equation run times. (b) Ratio of SSA to EMC run times. (c) Region in two dimensional (2D) parameter space where each method is optimal.

Image of FIG. 13.
FIG. 13.

Comparative run times for first passage on . (a) Ratio of SSA to master equation run times. (b) Ratio of SSA to EMC run times. (c) Region in 2D parameter space where each method is optimal.

Image of FIG. 14.
FIG. 14.

Pseudocode for AD for a simple path.

Image of FIG. 15.
FIG. 15.

(a) Comparative run times for first passage for ten trimer counts. Ratio of SSA to ME-AD run times. (b) Comparative run times for first passage for 100 trimer counts. Ratio of SSA to EMC-AD run times.

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/content/aip/journal/jcp/129/20/10.1063/1.3026595
2008-11-25
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Efficient stochastic sampling of first-passage times with applications to self-assembly simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/20/10.1063/1.3026595
10.1063/1.3026595
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