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-leaping: Accelerating the stochastic simulation algorithm by reaction leaps
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10.1063/1.2218339
/content/aip/journal/jcp/125/8/10.1063/1.2218339
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/8/10.1063/1.2218339

Figures

Image of FIG. 1.
FIG. 1.

Decaying-dimerizing reaction set [Eq. (30)]: histogram of the distribution of the species for for several values of the accuracy parameter .

Image of FIG. 2.
FIG. 2.

Decaying-dimerizing reaction set [Eq. (30)]: Cross plots of the computation time, histogram error and control parameter for -leaping (“엯” markers) and -leaping (“▿” markers).

Image of FIG. 3.
FIG. 3.

Low species reactions [Eq. (32)] speedup of -leaping relative to the SSA vs the relaxation parameter for (×), 0.01 (▿), 0.03 (엯), and 0.05 (+) in linear and logarithmic coordinates.

Image of FIG. 4.
FIG. 4.

Low species reactions [Eq. (32)]: error on the histogram of species 1 for the modified -leaping relative to the SSA vs the relaxation parameter for (×), 0.01 (▿), 0.03 (엯), and 0.05 (+) in linear and logarithmic coordinates.

Image of FIG. 5.
FIG. 5.

Low species reactions [Eq. (32)]: contours of the speedup and error of -leaping relative to the SSA vs the relaxation parameters and .

Image of FIG. 6.
FIG. 6.

Low species reactions [Eq. (32)]: histogram of species 1 for the SSA (엯), -leaping (∗), and -leaping for (◻), 0.08 (▿), and 0.4 (◇).

Image of FIG. 7.
FIG. 7.

LacZ/LacY model [Kierzek (Ref. 8)]: mean trajectories and standard deviations of four molecular species for the SSA (solid line) and the -leap method with , (dots).

Image of FIG. 8.
FIG. 8.

LacZ/LacY model, first cell generation ( to ): plot of the evolution of the number of binomial samples for one -leaping run (, , condition 1 for selection) with (solid) and without (dashed) sorting [step (5)]. When applied, the sorting is made every 10 000 time steps. The straight line indicates the mean value of (equal to 4.1) when the sorting is applied. The value of is monitored every 2500 time steps.

Image of FIG. 9.
FIG. 9.

LacZ/LacY model ( to ): histogram distance errors with respect to CPU times for runs. The modified Poisson (◻) algorithm with -selection formula of Ref. 6 [Eq. (3)] is plotted for to by steps of 0.01. The -leaping with condition 3 is plotted for , 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.75, for fixed values of (indicated under the figures), with (엯) and without (×) sorting.

Tables

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Algorithm 1: -sampling

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Algorithm 2: -sampling

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Algorithm 3: -sampling for systems with disparate rates

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Table I.

Low species reactions [Eq. (32)]: speedup relative to the SSA and average number of step per run for the - and -leaping alogrithms with . The values for the original Poisson (OP) and modified Poisson (MP) are taken from (Ref. 5).

Generic image for table
Table II.

LacZ/LacY model [Kierzek (Ref. 8)]: reaction channels and rates.

Generic image for table
Table III.

LacZ/LacY model [Kierzek (Ref. 8)]: speedup relative to the SSA (CPU time SSA/CPU time) for the computation of the first generation .

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/content/aip/journal/jcp/125/8/10.1063/1.2218339
2006-08-23
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/8/10.1063/1.2218339
10.1063/1.2218339
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