In this paper we propose a new numerical approach to the non stationary optical di usion tomography OT problem The assumption in the method is that the absorption and or di usion coe cients are non stationary in the sense that they may exhibit signi cant changes during the time that is needed to measure data for one traditional image frame In the proposed method OT problem is formulated as a st...

We present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection di usion equation ut r f u u The method is based on the use of operator splitting to isolate the convection part and the di usion part of the equation In the casem dimensional splitting is used to reduce the m dimensional convection problem to a series of one di...

Di usion Tensor Imaging (DTI) is a relatively new modality for human brain imaging. During the last years, this modality has become widely used in medical studies. Tractography is currently the favorite technique to characterize and analyse the structure of the brain white matter. Only a few studies have been proposed to group data of particular interest. Rather than working on extracted bers o...

We have measured the radon di!usion, solubility and permeability coe$cients of various foils being of interest for the Borexino experiment. The applied methods and instrumentation are described and the mathematical model for di!usion of Rn, including its decay, is outlined. A very strong in#uence of water on the Rn di!usion through nylon foils was found. The rather low Rn permeability for dry n...

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic 9 di$erential equations 3rst. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–di$usion 11 systems (non-Newtonian 3ltration systems) are establish...

We compared the behavior of the Hodgkin}Huxley (HH) model subjected to two input regimes: "rstly, discrete pulses from a Poisson process, and then to a di!usion approximation, constructed to share statistical properties with the discrete pulse input. The results show that under a wide range of physiologically plausible input conditions the di!usion process is equivalent to the pulse process, in...

The di usion orientation distribution function (ODF) can be reconstructed from q-ball imaging (QBI) to map the complex intravoxel structure of water di usion. As acquisition time is particularly large for high angular resolution di usion imaging (HARDI), fast estimation algorithms have recently been proposed, as an on-line feedback on the reconstruction accuracy. Thus the acquisition could be s...

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...

We develop a new framework to calibrate stochastic volatility option pricing models to an arbitrary prescribed set of prices of liquidly traded options. Our approach produces an arbitrage-free stochastic volatility di usion process that minimizes the distance to a prior di usion model. We use the notion of relative entropy (also known under the name of Kullback-Leibler distance) to quantify the...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...