Nuclear Spin‐Noise Spectra of Hyperpolarized Systems

Spin‐noise appeal : Detection of NMR spin‐noise is very appealing when dilute hyperpolarized species are considered. Continuous monitoring of the noise absorption at the Larmor frequency enables determination of T₁ and T₂*, independently of the static magnetic field. An inductively coupled microcoil located inside the NMR tube (see picture) allows acquisition of ¹²⁹Xe spin‐noise spectra without radio‐frequency excitation.

     

Highly sensitive optical humidity probe

A highly sensitive optical humidity probe based on reflectance measurements has been developed using Nafion^®-crystal violet (CV) films. This sensor can be used to calibrate relative humidity (RH) in the range 0-0.25% with a detection limit (blank signal + 3σ_b, where σ_b = the standard deviation (S.D.) of the blank signal) of 0.018% RH (∼4.37 ppm) and exhibited low hysteresis. The sensor films were fully reversible in dry nitrogen and reversal times were shown to be dependent on exposure time and % RH. The response to 1% RH was highly reproducible (S.D. = 1.67%, number of samples (n) = 5). Hydrogen chloride gas did not interfere with the response of the sensor to RH but did reduce sensor reversal times. This sensor displayed sufficient sensitivity that it could be used to detect ppm levels of moisture in process gases such as nitrogen and HCl.     

An Itô formula for a fractional Brownian sheet with arbitrary Hurst parameters

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the fractional Brownian sheet with arbitrary Hurst parameters .

     

Influence of noise and delay on reaction-diffusion recurrent neural networks

In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.     

Random attractor for the Ladyzhenskaya model with additive noise

This paper studies the dynamical behavior of the Ladyzhenskaya model with additive noise. With some conditions, we prove that the generated random dynamical system has a compact random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.     

On a topological closeness of perturbed Mandelbrot sets

In the present work we propose a numerical and visual tool for the study of the deformation of the Mandelbrot sets of perturbed Mandelbrot maps by noise in comparison with the original Mandelbrot set. Further, by employing these numerical tools, we support the invariance of the Mandelbrot set of a noise-perturbed Mandelbrot map under different noise realizations. Finally, we provide evidence for the non-fractal structure of the Mandelbrot set of a noise-perturbed Mandelbrot map.     

Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise

In this paper, we focus on the asymptotic behavior of the optimal filter where both signal and observation processes are driven by Lévy noises. Indeed, we study large deviations for the case where the signal-to-noise ratio is small by considering weak convergence arguments. To that end, we first prove the uniqueness of the solution of the controlled Zakai and Kushner–Stratonovich equations. For this, we employ a method which transforms the associated equations into SDEs in an appropriate Hilbert space. Next, taking into account the controlled analogue of Zakai and Kushner–Stratonovich equations, respectively, the large deviation principle follows by employing the existence, uniqueness and tightness of the solutions.     

An optimal Gauss–Markov approximation for a process with stochastic drift and applications

We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein–Uhlenbeck type process, by using direct methods of calculus of variations. We show that general power cost functionals satisfy the conditions for existence and uniqueness of the approximation. We provide some examples of general interest and we give bounds on the goodness of the corresponding approximations. Finally, we focus on a model of a neuron embedded in a simple network and we study the approximation of its activity, by exploiting the aforementioned results.     

Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Reaction-diffusion Equations

This paper dealswith non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s ∈ (0,1). We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.