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A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
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10.1063/1.4789612
/content/aip/journal/jcp/138/5/10.1063/1.4789612
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/5/10.1063/1.4789612

Figures

Image of FIG. 1.
FIG. 1.

Upper plot: The number of X molecules as a function of time. The stochastic process sequentially visits the two most probable states defined as the maxima of the PDF. Lower panel: RER as a function of time when k 1 A is perturbed by 0.05 computed using (28) (dashed line) and using (30) (grey line). In both cases, the accuracy of the numerical estimators increase as the number of samples increases.

Image of FIG. 2.
FIG. 2.

Upper plot: Exact (black), estimated by (28) (grey), and estimated by (30) (white) RER for various directions. k 2 is the most sensitive parameter followed by k 1 A while the least sensitive parameters are k 4 and k 3 B. Lower plot: RER when parameter θ k is perturbed by +ε0 (black), when perturbed by −ε0 (white) and when computed by FIM (grey).

Image of FIG. 3.
FIG. 3.

Upper plot: The stationary distributions for the unperturbed process (solid line), the most sensitive parameter k 2 (dashed line), and the least sensitive parameter k 3 B (dotted line). Lower plot: The stationary distributions for the unperturbed process (solid line), when the most sensitive parameter k 2 is perturbed (dashed line), and when the most sensitive direction εmax  is perturbed (dotted line).

Image of FIG. 4.
FIG. 4.

Upper plot: Relative entropy rate as a function of time for perturbations of D e (solid line), a (dashed line), and of r e (grey line) at the reversible regime (α = 0). The variance of the numerical RER is large, necessitating more samples for accurate estimation. Lower plot: RER for various directions where the most sensitive parameter is a. We observe that the FIM-based RER which is always positive has substantially less variance than the directly-computed numerical RER.

Image of FIG. 5.
FIG. 5.

Upper plots: Level sets (or neutral spaces) for the reversible case (α = 0). Lower plots: Level sets for the irreversible case (α = 0.1).

Image of FIG. 6.
FIG. 6.

Upper plot: Relative entropy rate as a function of time for perturbations of both k 1 (solid line) and of k 2 (dashed line). An equilibration time until the process reach its metastable regime is evident. Lower plot: RER for various directions. The most sensitive parameter is k 1.

Image of FIG. 7.
FIG. 7.

Typical configurations obtained by ε0-perturbations of the most and least sensitive parameters. The comparison with the reference configuration reveals the differences between the most and least sensitive perturbation parameters.

Image of FIG. 8.
FIG. 8.

Vector field with the most (solid arrows) and least (dashed arrows) sensitive directions computed from eigenvalue analysis of FIM. The length of the arrows is proportional to the corresponding eigenvalue.

Tables

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Table I.

The rate of the kth event when the number of X molecules is x is denoted by c k (x). Ω is the volume of the system.

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Table II.

Parameter values for the Schlögl model.

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Table III.

Parameter values for the discretized Langevin system.

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Table IV.

The rate of the kth event of the jth site given that the current configuration is σ is denoted by c k (j; σ) where n.n. stands for nearest neighbors.

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/content/aip/journal/jcp/138/5/10.1063/1.4789612
2013-02-06
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/5/10.1063/1.4789612
10.1063/1.4789612
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