Effects of external noise on the Swift-Hohenberg Equation

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bnard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Growth of unstable interfaces in disordered media

The effects of a disordered medium in the growth of unstable interfaces are studied by means of two local models with multiplicative and additive quenched disorder, respectively. For short times and large pushing the multiplicative quenched disorder is equivalent to a time-dependent noise. In this regime, the linear dispersion relation contains a destabilizing contribution introduced by the noise. For long times, the interface always gets pinned. We model the systematics of the pinned shapes by means of an effective nonlinear model. These results show good agreement with numerical simulations. For the additive noise we find numerically that a depinning transition occurs.

Correlation postprocessing-based method for the detection of de focused images

We present a method to detect patterns in defocused scenes by means of a joint transform correlator. We describe analytically the correlation plane, and we also introduce an original procedure to recognize the target by postprocessing the correlation plane. The performance of the methodology when the defocused images are corrupted by additive noise is also considered.

High capacity audio watermarking using the high frequency band of the wavelet domain

This paper proposes a novel high capacity robust audio watermarking algorithm by using the high frequency band of the wavelet decomposition at which the human auditory system (HAS) is not very sensitive to alteration. The main idea is to divide the high frequency band into frames and, for embedding, to change the wavelet samples depending on the average of relevant frame¿s samples. The experimental results show that the method has a very high capacity (about 11,000 bps), without significant perceptual distortion (ODG in [¿1 ,0] and SNR about 30dB), and provides robustness against common audio signal processing such as additive noise, filtering, echo and MPEG compression (MP3).

Decay of an unstable state in the presence of multiplicative noise

The phenomenon of anomalous fluctuations associated with the decay of an unstable state is analyzed in the presence of multiplicative noise. A theory is presented and compared with a numerical simulation. Our results allow us to distinguish the roles of additive and multiplicative noise in the nonlinear relaxation process. We suggest the use of experiments on transient dynamics to understand the effect of these two sources of noise in problems in which parametric noise is thought to be important, such as dye lasers.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Multiplicative noise effects on relaxations from marginal states

Relaxational processes in bistable potentials close to marginal conditions are studied under the combined effect of additive and multiplicative fluctuations. Characteristic time scales associated with the first-passage-time-distribution are analytically obtained. Multiplicative noise introduces large effects on the characteristic decay times, which is particularly significant when relaxations are mediated by fluctuations, i.e., below marginality and for small noise intensity. The relevance of our approach with respect to realistic chemical bistable systems experimentally operated under external noise influences is mentioned.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

Creació automàtica de gràfics estadístics a partir de dades de soroll d’Europa amb tecnologies Open Source en el visor Noise Map Viewer de l’ETC-LUSI

El projecte ha consistit en la creació de gràfics estadístics de soroll d’Europa de forma automàtica amb tecnologies Open Source dins el visor Noise Map Viewer per Europa de l’ETC-LUSI. La llibreria utilitzada per fer aquest procés ha estat JFreeChart i el llenguatge de programació utilitzat ha estat Java (programació orientada a objectes) dins l’entorn de desenvolupament integrat Eclipse. La base de dades utilitzada ha estat PostgreSQL. Com a servidors s’han fet servir Apache (servidor HTTP) i Tomcat (servidor contenidor d’aplicacions). Un cop acabat el procés s’ha integrat dins de MapFish canviant el codi JavaScript corresponent de la web original.

A Folk Theorem for Games when Frequent Monitoring Decreases Noise

This paper studies frequent monitoring in an infinitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length _. It shows that a limit folk theorem can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e., _. The approach assumes that the expected joint output depends exclusively on the action profile simultaneously and privately decided by the players at the beginning of each period of the game, but not on _. The strong decreasing effect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit. JEL: C72/73, D82, L20. KEYWORDS: Repeated Games, Frequent Monitoring, Public Monitoring, Brownian Motion.