Search results for " Divergence"
showing 10 items of 131 documents
Factorization of the soft gluon divergence from the dipole picture deep inelastic scattering cross sections at next-to-leading order
2018
We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the BK evolution equation. In the ca…
Kullback-Leibler distance as a measure of the information filtered from multivariate data
2007
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to s…
Strong field amplification of XUV: phase matching aspects
2011
The dependence of the yield of high-order harmonic generation (HHG) on several important experimental parameters has been successfully modeled in the last 20 years by taking into account the single atom response and propagation effects. We extended this description by adding a stimulated emission process and named it x-ray parametric amplification (XPA). Beyond the super-quadratic increase of the XUV signal, which can be explained only in a limited pressure range by HHG theory, other observed characteristics like exponential growth, gain narrowing, strong blue-shift, beam divergence, etc. and their dependence on laser intensity and gas pressure can be explained accurately only by the new XP…
Rigorous analysis of three-dimensional beam transmission through a dielectric slab
1997
The plane-wave-spectrum technique is applied to study the transmission of a three-dimensional beam through a dielectric slab. The electromagnetic beam radiated from an aperture antenna is represented by an angular spectrum of plane waves. The use of three different co-ordinate systems using rectangular co-ordinates allows a rigorous formulation to be obtained. The near field transmitted through a dielectric slab is obtained and compared with measurements.
Hierarchy and dynamics of trace distance correlations
2013
We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic expressions for the classical and total correlations. The ensuing hierarchy of correlations based on trace distance is compared to the ones based on relative entropy and Hilbert-Schmidt norm. Although some common features can be found, the trace distance measure is shown to differentiate from the others in that the closest uncorrelated state to a given bipartite quantum state is not given by the product of the marginals, and further, the total correlations are s…
Dynamics of geometric and entropic quantifiers of correlations in open quantum systems
2012
We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic quantifiers of the different kinds of correlations in a non-Markovian open two-qubit system under local dephasing. We find that qualitative differences occur only for quantum discords. This is taken to imply that geometric and entropic discords are not, in general, equivalent in describing the dynamics of quantum correlations. We then show that also geometric and entropic quantifiers of total correlations present qualitative disagreements in the state spa…
Preliminary insights into the molecular barcoding data of Turraea socotrana (Meliaceae) from Socotra (Yemen)
2020
The relationship of two geographically and ecologically separated populations of Turraea socotrana Styles and F. White (Meliaceae), a vulnerable and scattered shrub from the island of Socotra (Yemen), was explored using preliminary molecular data. The nuclear ribosomal ITS region was used to screen the level of genetic divergence of T. socotrana from ecologically distant localities in comparison to a few other species of Turraea and closely related genera. The individuals from the inland (Diksam) differed from the western coastal ones (Ma’alah) by vegetative characters and by the rbcL gene. This may be due to the fact that the population from Ma’alah grows on lithosoil slopes directly expos…
Generalized Harnack inequality for semilinear elliptic equations
2015
Abstract This paper is concerned with semilinear equations in divergence form div ( A ( x ) D u ) = f ( u ) , where f : R → [ 0 , ∞ ) is nondecreasing. We introduce a sharp Harnack type inequality for nonnegative solutions which is a quantified version of the condition for strong maximum principle found by Vazquez and Pucci–Serrin in [30] , [24] and is closely related to the classical Keller–Osserman condition [15] , [22] for the existence of entire solutions.
Tetrolet-based reduced reference image quality assessment approach
2014
In this paper, we propose a new reduced reference image quality assessment (RRIQA) scheme. For this purpose, we use a statistical-based method in a new adaptive Haar wavelet transform domain, called Tetrolet. Firstly, we decompose the reference and distorted images and we obtain the Tetrolet coefficients for each image. Secondly, we use a marginal Generalized Gaussian Density (GGD) to model each subband coefficients. Finally, the distortion measure is computed using the Kullback Leibler Divergence (KLD) between GGD Probability density function (PDFs). Experimental results show the efficiency of the proposed method when comparing to those reported in the literature.
On the Choice of the Most Suitable Period to Map Hill Lakes via Spectral Separability and Object-Based Image Analyses
2023
Technological advances in Earth observation made images characterized by high spatial and temporal resolutions available, nevertheless bringing with them the radiometric heterogeneity of small geographical entities, often also changing in time. Among small geographical entities, hill lakes exhibit a widespread distribution, and their census is sometimes partial or shows unreliable data. High resolution and heterogeneity have boosted the development of geographic object-based image analysis algorithms. This research analyzes which is the most suitable period for acquiring satellite images to identify and delimitate hill lakes. This is achieved by analyzing the spectral separability of the su…