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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… (More)

- Narmada Herath, Domitilla Del Vecchio
- CDC
- 2016

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 as the singular perturbation parameter, we obtain a reduced order model that approximates the slow variable… (More)

- Narmada Herath, Domitilla Del Vecchio
- ACC
- 2016

Systems with multiple time-scales can be written in singular perturbation form, where the dynamics are separated into slow and fast, with a small parameter ✏ capturing the separation in time-scales. The analysis of singularly perturbed systems consists of obtaining a reduced-order model that approximates the dynamics of the system when the timescale… (More)

- Narmada Herath, Domitilla Del Vecchio
- ACC
- 2014

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,… (More)

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… (More)

- Gérard Laurent, Claire Bernhard, +21 authors Stéphane Roux
- Nanoscale
- 2016

Many studies have been devoted to adapting the design of gold nanoparticles to efficiently exploit their promising capability to enhance the effects of radiotherapy. In particular, the addition of magnetic resonance imaging modality constitutes an attractive strategy for enhancing the selectivity of radiotherapy since it allows the determination of the most… (More)

In this paper, we consider the problem of model order reduction for a class of singularly perturbed stochastic differential equations with linear drift terms. We present a reduced-order model that approximates both slow and fast variable dynamics when the time-scale separation is large. Specifically, we show that, on a finite time interval, the moments of… (More)

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