Neural information processing models largely assume that the samples for training a neural network are sufficient. Otherwise there exist a non-negligible error between the real function and estimated function from a trained network. To reduce the error in this paper we suggest a diffusion-neural-network (DNN) to learn from a small sample. First, we show the principle of information diffusion us...

The Gaussian Diffusion Approximation proposes that the distribution of displacements Δx for a particle diffusing through a complex fluid has a Gaussian dependence on Δx. We demonstrate from experimental evidence and computer simulations that this approximation is generally incorrect in complex fluids. As a result, experimental studies that have used the Gaussian Diffusion Approximation to inter...

A somewhat recent extension to traditional MRI imaging techniques, Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) measures the self-diffusion of water in biological tissue. Neural fiber tracts contain bundles of parallel axons whose membranes restrict diffusion, so the self-diffusion of water occurs preferentially along the tracts. Thus in DT-MRI imagery of the brain, each diffusion tenso...

Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that there is a large class of one-dimensional diffusion processes for which it is possible to give conven...

The machine repair problem with spares and additional repairman is analyzed. The interfailure and repair times of the units are general identical and independently distributed. The failure and repair rates are assumed to be state dependent. Using diffusion approximation technique, we obtain the queue size distribution under steady state. The average number of failed units, average number of ope...

A photon-transport forward model for image reconstruction in turbid media is derived that treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation. This model can conveniently replace the commonly used diffusion approximation in optical tomography. An analytical expression of the background Green's function is obtained from the cumulant solution of t...