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In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation form, with ε as the singular perturbation parameter, we obtain a reduced order model that approximates the slow variable dynamics of the original system. In particular,...
We consider a class of stochastic differential equations in singular perturbation form, where the drift terms are linear and diffusion terms are nonlinear functions of the state variables. In our previous work, we approximated the slow variable dynamics of the original system by a reduced-order model when the singular perturbation parameter ∊ is small. In this work, we obtain an approximation for...
We consider a class of singularly perturbed stochastic differential equations with linear drift and nonlinear diffusion terms. We obtain a reduced-order model that approximates the slow variable dynamics of the original system when the singular perturbation parameter e is small. In our previous work, it was shown that, on a finite time interval, the first and the second moments of the slow variable...
A class of singularly perturbed stochastic differential equations (SDE) with linear drift and nonlinear diffusion terms is considered. We prove that, on a finite time interval, the trajectories of the slow variables can be well approximated by those of a system with reduced dimension as the singular perturbation parameter becomes small. In particular, we show that when this parameter becomes small...
At the interconnection of two gene transcriptional components in a biomolecular network, the noise in the downstream component can be reduced by increasing its gene copy number. However, this method of reducing noise increases the load applied to the upstream system, called retroactivity, thereby causing a perturbation in the upstream system. In this work, we quantify the error in the system trajectories...
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