Search results for "Gaussia"
showing 10 items of 653 documents
Structure of longitudinal chromomagnetic fields in high energy collisions
2014
We compute expectation values of spatial Wilson loops in the forward light cone of high-energy collisions. We consider ensembles of gauge field configurations generated from a classical Gaussian effective action as well as solutions of high-energy renormalization group evolution with fixed and running coupling. The initial fields correspond to a color field condensate exhibiting domain-like structure over distance scales of order the saturation scale. At later times universal scaling emerges at large distances for all ensembles, with a nontrivial critical exponent. Finally, we compare the results for the Wilson loop to the two-point correlator of magnetic fields.
Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems
2023
Abstract For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data and an optimizer, e.g. a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to pr…
A Simple Noise Model with Memory for Biological Systems
2005
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We …
An Interactive Framework for Offline Data-Driven Multiobjective Optimization
2020
We propose a framework for solving offline data-driven multiobjective optimization problems in an interactive manner. No new data becomes available when solving offline problems. We fit surrogate models to the data to enable optimization, which introduces uncertainty. The framework incorporates preference information from a decision maker in two aspects to direct the solution process. Firstly, the decision maker can guide the optimization by providing preferences for objectives. Secondly, the framework features a novel technique for the decision maker to also express preferences related to maximum acceptable uncertainty in the solutions as preferred ranges of uncertainty. In this way, the d…
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…
Visual saliency detection in colour images based on density estimation
2017
International audience; A simple and effective method for visual saliency detection in colour images is presented. The method is based on the common observation that local salient regions exhibit distinct geometric and and texture patterns from neighbouring regions. We model the colour distribution of local image patches with a Gaussian density and measure the saliency of each patch as the statistical distance from that density. Experimental results with public datasets and comparison with other state-of-the-art methods show the effectiveness of our method.
Quadrature effects on the accuracy of flux calculations in realistic atmospheres
1993
Abstract We have investigated the accuracy of five different quadrature methods—equal steps in θ, equal steps in cos θ, Gaussian, double Gaussian and Gauss-Lobatto—on the accuracy of fluxes in realistic aerosol atmospheres, using the Gauss-Seidel method. In addition, a range of Gaussian quadrature stream numbers from two to 32 were compared. The atmospheric models considered are those recently presented by Lenoble, with the exception that we have used Henyey-Greenstein phase functions in place of Mie. Our results should be easily reproduceable by any other workers interested in similar realistic atmospheres. A table of Gauss-Lobatto weights and points is provided as an appendix.
Probabilistic Self-Localization and Mapping - An Asynchronous Multirate Approach
2008
[EN] In this paper, we present a set of robust and efficient algorithms with O(N) cost for the solution of the Simultaneous Localization And Mapping (SLAM) problem of a mobile robot. First, we introduce a novel object detection method, which is mainly based on multiple line fitting method for landmark detection with regular constrained angles. Second, a line-based pose estimation method is proposed, based on LeastSquares (LS). This method performs the matching of lines, providing the global pose estimation under assumption of known Data-Association. Finally, we extend the FastSLAM (FActored Solution To SLAM) algorithm for mobile robot self-localisation and mapping by considering the asynchr…
Highlighting numerical insights of an efficient SPH method
2018
Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered …
Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality
2016
We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.