Estimating the risk of extinction is one of the central foci of conservation biology, but such estimates are often constrained by the available data. In the face of limited data, several authors have suggested using diffusion approximations to estimate the mean time to extinction as a means of quantifying the risk of extinction. However, the accuracy of the diffusion approximation for character...

Min et al. (2009) presented two complementary techniques that use the diffusion approximation to allow efficient Monte-Carlo radiation transfer in very optically thick regions: a modified random walk and a partial diffusion approximation. In this note, I show that the calculations required for the modified random walk method can be significantly simplified. In particular, the diffusion coeffici...

Traditionally, the radiative transfer equation and its diffusion approximation are derived for a medium with a spatially constant refractive index (Ishimaru 1978 Wave Propagation and Scattering in Random Medial vol 1 (New York: Academic)). In this paper, we derive the radiative transport equation and its diffusion approximation relevant to optical tomography for a medium with a spatially varyin...

In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the d...

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a diffusion process at a fixed deterministic date and the second one concerns the law of a stochastic approximation algorithm at a given time-step. Our results ...

Currently, we are developing a computational optical biopsy technology for molecular sensing. We use the diffusion equation to model photon propagation but have a concern about the accuracy of diffusion approximation when the optical sensor is close to a bioluminescent source. We derive formulas to describe photon fluence for point and ball sources and measurement formulas for an idealized opti...

The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SP(N)) approximation for orders ...

We explicitly calculate the aggregate diffusion dynamics in one-dimensional agent-based models of adoption of new products, without using the mean-field approximation. We then introduce a clusters-dynamics approach, and use it to derive an analytic approximation of the aggregate diffusion dynamics in multidimensional agent-based models. The clusters-dynamics approximation shows that the aggrega...

We derive an analytical weak approximation of a multidimensional diffusion process as coefficients or time are small. Our methodology combines the use of Gaussian proxys to approximate the law of the diffusion and a Finite Element interpolation of the terminal function applied to the diffusion. We call this method Stochastic Approximation Finite Element (SAFE for short) method. We provide error...