Search results for "Gauss"

Gaussian plane and spherical means in separable Hilbert spaces

1982

Sensitivity analysis of Gaussian processes for oceanic chlorophyll prediction

2015

Gaussian Process Regression (GPR) for machine learning has lately been successfully introduced for chlorophyll content mapping from remotely sensed data. The method provides a fast, stable and accurate prediction of biophysical parameters. However, since GPR is a non-linear kernel regression method, the relevance of the features are not accessible. In this paper, we introduce a probabilistic approach for feature sensitivity analysis (SA) of the GPR in order to reveal the relative importance of the features (bands) being used in the regression process. We evaluated the SA on GPR ocean chlorophyll content prediction. The method revealed the importance of the spectral bands, thus allowing the …

Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach

2011

In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.

Non Linear Systems Under Complex α-Stable Le´vy White Noise

2003

The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME

Stochastic Response on Non-Linear Systems under Parametric Non-Gaussian Agencies

1992

The probabilistic response characterization of non-linear systems subjected to non-normal delta correlated parametric excitation is obtained. In order to do this an extension of both Ito’s differential rule and the Fokker-Planck equation is presented, enabling one to account for the effect of the non-normal input. The validity of the approach reported here is confirmed by results obtained by means of a Monte Carlo simulation.

Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime

1996

We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…

1973

The direct and the inverse problem of the light scattering from dilute polymer solutions is solved for GAUssian coils at the theta point. Theoretical scattering functions and their derivatives are analytically calculated for the general gamma distribution of molecular weights as a function of the non-uniformity and the weight average molecular weight, and also for various ratios of the statistical segment length of the coil to the wave length of the scattered light. The asymptote and the tangent of P are obtained by analysing the operator in the ZIMM equation and their mutual position is compared in the angle range 150° to 180°. The scattering envelopes of microgel systems are analytically …

Stochastic linearization for the response of MDOF systems subjected to external and parametric Gaussian excitations

1991

The stochastic linearization approach is examined for the most general case of non zero-mean response of non-linear MDOF systems subjected to parametric and external Gaussian white excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. Moreover, an extension of the Atalik-Utku approach to non zero-mean response systems allows to obtain simple formulations for the linearized drift coefficients. Some applications show the good accuracy of the method.

Quenched and annealed free energies

1984

This paper gives a simple exposition of the Nishimori method to solve certain quenched, random bond spin-glass models. It allows a transparent physical interpretation in terms of annealed systems. As an application a special solution of the Sherrington-Kirkpatrick model with a discrete probability distribution is obtained and shown to agree with the solution for the Gaussian case. This substantiates the claim that the averaged free energy does not depend on the details of the probability distribution Expose simple de la methode de Nishimori pour resoudre certains modeles de verres de spin avec interactions aleatoires. Interpretation transparente en termes de systemes recuits. Presentation d…

Application of Periodic Frames to Image Restoration

2014

In this chapter, we present examples of image restoration using periodic frames. Images to be restored were degraded by blurring, aggravated by random noise and random loss of significant number of pixels. The images are transformed by periodic frames designed in Sects. 17.2 and 17.4, which are extended to the 2D setting in a standard tensor product way. In the presented experiments, performances of different tight and semi-tight frames are compared between each other in identical conditions.