The formation of pattern in biological systems may be modeled by a set of reaction-diffusion equations. A diffusion-type coupling operator biologically significant in neuroscience is a difference of Gaussian functions (Mexican Hat operator) used as a spatial-convolution kernel. We are interested in the difference among behaviors of stochastic neural field equations, namely space-time stochastic...

Stochastic generators of completely positive and contractive quantum stochastic convolution cocycles on a C∗-hyperbialgebra are characterised. The characterisation is used to obtain dilations and stochastic forms of Stinespring decomposition for completely positive convolution cocycles on a C∗-bialgebra. Stochastic (or Markovian) cocycles on operator algebras are basic objects of interest in qu...

We investigate the long term behavior of solutions to a stochastic Volterra integro-differential equation with a fading memory; the fading memory is represented by using a decaying exponential convolution kernel. We give sufficient conditions for asymptotic mean square stability of the solution. In a similar spirit, we investigate the long term behavior of solutions to discrete analogues of the...

Line Integral Convolution (LIC) is a common approach for the visualization of 2 0 vector fields. It is well suited for visualizing the direction of a flow field, but it gives no information about the orientation of the underlying vectors. We introduce Oriented Line Integral Convolution (OLIC), where direction as well as orientation are encoded within the resulting image. This is achieved b y us...

In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the asymptotic properties of this solution. We first study the nonlinear stochastic heat equation. A central special case is the parabolic Ander...

Line Integral Convolution (LIC) is a common approach for the visualization of vector elds. It is well suited for visualizing the direction of a ow eld, but it gives no information about the orientation of the underlying vectors. We introduce Oriented Line Integral Convolution (OLIC), where direction as well as orientation are encoded within the resulting image. This is achieved by using a low f...

In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

In this paper we look at the Line Integral Convolution method for flow visualization and ways in which this can be applied to the visualization of two dimensional, steady flow fields in the presence of uncertainty. To achieve this, we start by studying the method and reviewing the history of modifications other authors have made to it in order to improve its efficiency or capabilities, and usin...