Search results for "Nonlinear system"
showing 10 items of 1446 documents
A shoreline boundary condition for a highly nonlinear Boussinesq model for breaking waves
2012
Abstract A physically based strategy was used to model swash zone hydrodynamics forced by breaking waves within a Boussinesq type of model. The position and the velocity of the shoreline were determined continuously in space by solving the physically-based equations of the shoreline motion; moreover, a fixed grid method, with a wet–dry interface, was adopted for integrating the Boussinesq model. The numerical stability of the model was improved by means of an extrapolation method. To validate the proposed methodology, the classical analytical solution for the shoreline motion of a monochromatic wave train over a plane beach was considered. The comparison between the analytical and numerical…
Probabilistic stability analysis of social obesity epidemic by a delayed stochastic model
2014
Abstract Sufficient conditions for stability in probability of the equilibrium point of a social obesity epidemic model with distributed delay and stochastic perturbations are obtained. The obesity epidemic model is demonstrated on the example of the Region of Valencia, Spain. The considered nonlinear system is linearized in the neighborhood of the positive point of equilibrium and a sufficient condition for asymptotic mean square stability of the zero solution of the constructed linear system is obtained.
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …
2014
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…
Kernel image similarity criterion
2011
This paper presents a family of metrics for assessing image similarity. The methods use the Hilbert-Schmidt Independence Criterion (HSIC) to estimate nonlinear statistical dependence between multidimensional images. The proposed methods have very good theoretical and practical properties. We illustrate the performance in evaluating the quality of natural photographic images, hyperspectral images under different noise levels, in synthetic multiresolution problems, and real pansharpening products.
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
2014
A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…
A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
1999
In this paper we summarize the main features of a new time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin, Osher and Fatemi. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on an ENO Hamilton-Jacobi version of Roe's scheme. We show numerical evidence of the speed, resolution and stability of this simple explicit procedure in two representative 1D and 2D numerical examples.
Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis
2016
Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance…
Retrieval of coloured dissolved organic matter with machine learning methods
2017
The coloured dissolved organic matter (CDOM) concentration is the standard measure of humic substance in natural waters. CDOM measurements by remote sensing is calculated using the absorption coefficient (a) at a certain wavelength (e.g. 440nm). This paper presents a comparison of four machine learning methods for the retrieval of CDOM from remote sensing signals: regularized linear regression (RLR), random forest (RF), kernel ridge regression (KRR) and Gaussian process regression (GPR). Results are compared with the established polynomial regression algorithms. RLR is revealed as the simplest and most efficient method, followed closely by its nonlinear counterpart KRR.
Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models
2020
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually a…
Efficient Nonlinear RX Anomaly Detectors
2020
Current anomaly detection algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed-Xiaoli (RX) method for anomaly detection by approximating the kernel function with either {\em data-independent} random Fourier features or {\em data-dependent} basis with the Nystr\"om approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost and they perform similar (or outperform) the standard kernel RX algorithm thanks t…