Stable nite di erence approximations of convection-di usion equations lead to large sparse linear systems of equations whose coe cient matrix is an M{matrix, which is highly non symmetric when the convection dominates. For an e cient iterative solution of such systems, it is proposed to consider in the non symmetric case an algebraic multilevel preconditioning method formerly proposed for pure ...

We derive hydrodynamic equations for systems not in local thermodynamic equilibrium, that is, where the local stationary measures are \non-Gibbsian" and do not satisfy detailed balance with respect to the microscopic dynamics. As a main example we consider the driven di usive systems(DDS), such as electrical conductors in an applied eld with di usion of charge carriers. In such systems, the hyd...

This paper studies the problem of diiusion in Markovian models, such as hidden Markov models (HMMs) and how it makes very diicult the task of learning of long-term dependencies in sequences. Using results from Markov chain theory, we show that the problem of diiusion is reduced if the transition probabilities approach 0 or 1. Under this condition, standard HMMs have very limited modeling capabi...

We consider a reaction–di usion equation in a bounded domain O⊂Rd, driven by a space– time white noise, with a drift term having polynomial growth and a di usion term which is not boundedly invertible, in general. We are showing that the transition semigroup corresponding to the equation has a regularizing e ect. More precisely, we show that it maps bounded and Borel functions de ned in the Hil...

Models of animal movement are necessary both as unambiguous descriptions of particular movement patterns and as starting points for the interpretation of observations on location. Radio-tracking, with frequent sampling so that successive observations are dependent, is an important special case to which only a single narrow class of models has been applied. The standard approach uses a bivariate...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

This paper describes a technique for determining a classi cation map or a hypothesis selection map using a system of reaction-di usion equations. The reaction term of the equations is a replicator equation and provides a mutually exclusive solution. The diffusion term exploits the local consistency of the solution. The technique is e cient for problems with a small labeling space compared to an...

For strongly directed anisotropic di usion ltering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic di usion. It applies recently discovered di erentiation lters with optimal rotation invariance [11], and comes down to an explicit scheme on a 5 5 stencil. By comparing it with severa...

The spatial resolution of an optical device is generally characterized by either the Point Spread Function (PSF) or the Modulation Transfer Function (MTF). To directly obtain the PSF one needs to measure the response of an optical system to a point light source. We present data that show the response of a back-illuminated CCD to light emitted from a sub-micron diameter glass ber tip. The potent...