This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a non degenerate α-stable limit, as the intensity of the underlying point process goes to infinity. More precisely, fin...

We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the It6 or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching betwee...

Spontaneous fluctuations in the electrical signals of the retina's photoreceptors impose a fundamental limit on visual sensitivity. While noise in the rods has been studied extensively, relatively little is known about the noise of cones. We show that the origin of the dark noise in salamander cones varies with cone type. Most of the noise in long wavelength-sensitive (L) cones arose from spont...

Using key tools such as Itô’s formula for general semimartingales, Kunita’s moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable. Keywords; stochastic differential equ...

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produce...

Noise is the primary visibility limit in the process of non-linear image enhancement, and is no longer a statistically stable additive noise in the post-enhancement image. Therefore novel approaches are needed to both assess and reduce spatially variable noise at this stage in overall image processing. Here we will examine the use of edge pattern analysis both for automatic assessment of spatia...

The universal approximation theorem for neural networks says that any reasonable function is well-approximated by a two-layer neural network with sigmoid gates but it does not provide good bounds on the number of hidden-layer nodes or the weights. However, robust concepts often have small neural networks in practice. We show an efficient analog of the universal approximation theorem on the bool...

Stochastic partial differential equations (SPDEs) whose solutions are probabilitymeasure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing trad...

A strong negation in da Costa’s Cn systems can be naturally extended from the strong negation (¬∗) of C1. In [1] Newton da Costa proved the conectives {→, ∧, ∨, ¬∗} in C1 satisfy all schemas and inference rules of classical logic. In the following paper we present a proof that all logics in the Cn herarchy also behave classically as C1. This result tell us the existance of a common property amo...

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one wi...