Sentence examples for a Gaussian diffusion from inspiring English sources

At medium b values (M) (100-1000 s/mm2), signal decay usually shows a Gaussian diffusion behavior, which would result in linear decay of the natural logarithm of the DWI signal intensity (SI) as the b-value increases, and subsequent quantification can be performed using a mono exponential analysis.

Norman (1975) relaxed this assumption with a Gaussian diffusion approximation in which mutant frequencies are centered about their deterministic trajectory with asymptotically normal deviations attributable to random genetic drift.

A model of enhanced generality is developed by assuming the real noise as the first component of an output of a linear filter system a zero-mean stationary Gaussian diffusion vectoral process, which conforms to the detailed balance condition.

This is because the infinitesimal mean of the Gaussian diffusion is not a function of N and therefore increasing the effective population size would not help to explain the rapid rise in mutant frequency (see Equation 3 in Methods).

Siemens Flash3D [4] makes use of the Gaussian diffusion method that, for a forward-projection, proceeds as follows.

Another useful application of the multi-population path integral (3.28) is that it provides a direct method for obtaining a Gaussian or diffusion approximation of the stochastic hybrid system, equivalent to the one obtained using the more complicated QSS reduction [27].

In this paper we have shown contralateral connections between the cerebellum and the prefrontal, frontal and parietal cortices via the thalamus in humans in vivo, which we achieved by implementing a pipeline with two key points: the selection of a non-Gaussian diffusion model and the definition of a seed and a target ROI (Palesi et al. 2013).

In Gaussian diffusion approximation, the mean square displacement (MSD) of diffusing molecules is linearly proportional to the diffusion coefficient D and the time t during which the diffusion process is observed [ 56]: (1) MSD = 2 N D t, where N is the "dimensionality" of the space over which diffusion distances are measured.

While the moments derived under the assumptions of the Gaussian diffusion will be inappropriate when selection is strong, a normal approximation of the transition distribution is still reasonable.

Norman (1975) derived an alternative approximation to the Wright Fisher process, known as the Gaussian diffusion, in which the effects of selection and mutation die off less rapidly compared to genetic drift as the population size gets larger and the selection and mutation parameters tend to zero.

Figure 1D, which plots the Kullback Leibler divergence of each approximate distribution from the exact distribution, demonstrates the superior performance of our method compared to the standard and Gaussian diffusion approximations under strong positive and negative selection in a large population with an initial mutant frequency of 0.5.