Gaussian Correlation Research Articles

해수면에 의한 신호 응답 강도의 시변동성 특성이 적용된 벨홉 기반의 수중음향 통신 채널 모델링 및 수동 시역전 통신 응용

본 논문은 시변 해수면을 생성하고 KA(Kirchhoff Approximation) 기반으로 산란계수를 시뮬레이션하여 결정론적 모델인 벨홉 임펄스 응답에 적용함으로써 시변동성 채널을 생성한다. 1D Pierson-Moskowitz 해수면 스펙트럼과 가우시안 상관 함수를 이용하여 일정한 속도로 변화하는 시 변동성 해수면을 사용하였다. 산란계수는 벨홉의 채널 임펄스 응답의 신호 응답 강도에 적용한다. 실제 실측 데이터에서 해수면 반사 성분을 분리하여 시 변동성 특성에 대한 도플러 파워 스펙트럼을 구하고, 해수면 산란계수 시뮬레이션의 결과와 비교하여 해수면에 사용된 가우시안 상관 함수의 상관 시간을 추정하였다. 최종적으로 생성된 시변동성 채널에 수동 시역전 통신 시나리오를 가정하고 기법을 적용하여 비트에러율 및 채널응답 상관계수 시뮬레이션을 수행하였다. This paper represents generation of time-varying underwater acoustic channels by performing scattering simulation with time-varying ocean surface and Kirchhoff approximation. In order to estimate the time-varying ocean surface, 1D Pierson-Moskowitz ocean power spectrum and Gaussian correlation function were used. The computed scattering coefficients are applied to the amplitudes of each impulse of BELLHOP simulation result. The scattering coefficients are then compared with measured doppler spectral density of signal components which were scattered from ocean surface and the correlation time used in the Gaussian correlation function was estimated by the comparison. Finally, bit-error-rate and channel correlation simulations were performed with the generated time-varying channel based on passive time-reversal communication scenario.

Effect of impurities on the transition temperature of a dilute dipolar trapped Bose gas

By using two-fluid model the effect of impurities on the transition temperature of a dipolar trapped Bose gas is investigated. By treating Gaussian spatial correlation for impurities from the interaction modified spectra of the system, the formula for the shift of transition temperature is derived. The shift of the transition temperature contains essentially three contributions due to contact, dipole-dipole and impurity interactions. Applying our results to Dipolar Bose gases show that the shift of the transition temperature due to impurities could be measured for isotropic trap (dipole-dipole contributions is zero) and Feshbach resonance technique (contact potential contribution is negligible).

Accuracy Analysis of Agriculture Soil Surface Roughness Parameter

Agricultural soil surface roughness parameters including surface root mean square height(rms h)and surface correlation length(cl)are key for effectively explaining radar backscattering coefficient and passive microwave brightness temperature,and its measurement accuracy is affected by measured method,measured instruments and data preprocessing.For surface roughness field measurement,the urgent problem is how to evaluate its measurement accuracy.This paper uses two-dimension surface height data from laser scanner and one-dimensional surface height data from Monte Carlo simulation,and analyzes the factors which influence the accuracy of surface roughness including sampling times,sampling interval,profile length,correlation function and large-scale structure(data skew and row structure).Four regions with different surface rough condition are used in this paper for analyzing surface roughness measurement method and accuracy.The result shows that,the measurement accuracy of agriculture soil surface roughness is about 80% under the condition of more than 20 samples,less than 10mm sampling interval and more than 200 cl profile length;the agreement between fractal correlation function and experimental spatial correlation coefficient is higher than Gaussian and exponential correlation function;and the skew and row structure of surface height data seriously affect the result of surface roughness parameter which needs to be removed before surface roughness calculation.

Study on the distribution properties of image plane speckle fields produced by Gaussian correlation weak scattering screens

Far-field speckle generated by weak scattering screen is a central bright spots, around which is a speckle structure similar to the normal speckle. According to the far-field speckle produced by weak scattering screen, it is assumed that the image plane speckle of weak scattering screen is the result of coherent superposition of both uniform background and normal speckle. However, there exists a discrepancy between the assumption and the actual image plane speckle. Based on the above circumstances, the statistical properties are studied about the image plane speckle fields produced by Gaussian correlation weak scattering screens in the 4f optical imaging system of high-pass filter. It is found that the above assumption is correct when the surface roughness of the weak scattering screen and the wavelength of the incident light wave are almost the same.

Testing noisy numerical data for monotonic association

Rank correlation measures are intended to measure to which extent there is a monotonic association between two observables. While they are mainly designed for ordinal data, they are not ideally suited for noisy numerical data. In order to better account for noisy data, a family of rank correlation measures has previously been introduced that replaces classical ordering relations by fuzzy relations with smooth transitions—thereby ensuring that the correlation measure is continuous with respect to the data. The given paper briefly repeats the basic concepts behind this family of rank correlation measures and investigates it from the viewpoint of robust statistics. Then, on this basis, we introduce a framework of novel rank correlation tests. An extensive experimental evaluation using a large number of simulated data sets is presented which demonstrates that the new tests indeed outperform the classical variants in terms of type II error rates without sacrificing good performance in terms of type I error rates. This is mainly due to the fact that the new tests are more robust to noise for small samples. The Gaussian rank correlation estimator turned out to be the best choice in situations where no prior knowledge is available about the data, whereas the new family of robust gamma test provides an advantage in situations where information about the noise distribution is available. An implementation of all robust rank correlation tests used in this paper is available as an R package from the CRAN repository.

Statistically modified surfaces: Experimental solutions for controlled scattered light

An experimental process is proposed to fabricate random rough surfaces which statistical properties can be controlled and tuned. The theoretical approach is developed opening the way to simple, low cost and large surface patterning method. A photoresist is exposed to a speckle pattern created from an argon ion laser. The laser beam has previously been shaped using a digital micromirror device, allowing controlling the correlation function of the speckle. The patterned resist is then transfer by reactive ion etching onto silicon, allowing use for optoelectronics applications. Examples of surfaces, fabricated with Gaussian and non-Gaussian (modified) correlation functions are shown and demonstrate an agreement with theoretical predictions.

Measuring Gaussian Quantum Information and Correlations Using the Rényi Entropy of Order 2

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.

Critical dynamics in systems controlled by fractional kinetic equations

The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions.Existence of the dissipative scaling regime in the framework of the ε expansion for σ=2, α=1/l,l=1,2,… is proved. Requirement of the continuous dependence of the critical exponents on α imposes the condition m=3.The main quantitative result is the calculation of the dynamical critical exponent z for α=1/2 up to ε2. We have obtained for it the expression z(1/2)=4+0.1555ε2+O(ε3).

Scattering by Anisotropic Rough Layered 2D Interfaces

We propose a statistical study of the scattering of an incident plane wave by a stack of two two-dimensional rough interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fields are represented by Rayleigh expansions, and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes. For slightly rough interfaces with a finite extension, we show that the modulus of the co- and cross-polarized scattering amplitudes follows a Hoyt law and that the phase is not uniformly distributed. For interfaces with an infinite extension, the modulus follows a Rayleigh law and the phase is uniformly distributed. We show that these results are true for correlated or uncorrelated interfaces and for isotropic or anisotropic interfaces.

Moving Kriging reconstruction for high-order finite volume computation of compressible flows

This paper describes the development of a high-order finite volume method for the solution of compressible viscous flows on unstructured meshes. The novelty of this approach is based on the use of moving Kriging shape functions for the computation of the derivatives in the numerical flux reconstruction step at the cell faces. For each cell, the successive derivatives of the flow variables are deduced from the interpolation function constructed from a compact stencil support for both Gaussian and quartic spline correlation models. A particular attention is paid for the study of the influence of the correlation parameter onto the accuracy of the numerical scheme. The effect of the size of the moving Kriging stencil is also investigated. Robustness and convergence properties are studied for various inviscid and viscous flows. Results reveal that the moving Kriging shape function can be considered as an interesting alternative for the development of high-order methodology for complex geometries.

Local Gaussian correlation: A new measure of dependence

It is a common view among finance analysts and econometricians that the correlation between financial objects becomes stronger as the market is going down, and that it approaches one when the market crashes, having the effect of destroying the benefit of diversification. The purpose of this paper is to introduce a local dependence measure that gives a precise mathematical description and interpretation of such phenomena. We propose a new local dependence measure, a local correlation function, based on approximating a bivariate density locally by a family of bivariate Gaussian densities using local likelihood. At each point the correlation coefficient of the approximating Gaussian distribution is taken as the local correlation. Existence, uniqueness and limit results are established. A number of properties of the local Gaussian correlation and its estimate are given, along with examples from both simulated and real data. This new method of modelling carries with it the prospect of being able to do locally for a general density what can be done globally for the Gaussian density. In a sense it extends Gaussian analysis from a linear to a non-linear environment.

Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties

The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI), I(X,Y), between random variables X,Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets of joint constraints leads to a hierarchy of lower MI bounds increasingly approaching the true MI. In particular, using standard bivariate Gaussian marginal distributions, it allows for the MI decomposition into two positive terms: the Gaussian MI (Ig), depending upon the Gaussian correlation or the correlation between ‘Gaussianized variables’, and a non‑Gaussian MI (Ing), coinciding with joint negentropy and depending upon nonlinear correlations. Joint moments of a prescribed total order p are bounded within a compact set defined by Schwarz-like inequalities, where Ing grows from zero at the ‘Gaussian manifold’ where moments are those of Gaussian distributions, towards infinity at the set’s boundary where a deterministic relationship holds. Sources of joint non-Gaussianity have been systematized by estimating Ing between the input and output from a nonlinear synthetic channel contaminated by multiplicative and non-Gaussian additive noises for a full range of signal-to-noise ratio (snr) variances. We have studied the effect of varying snr on Ig and Ing under several signal/noise scenarios.

Edge universality of correlation matrices

Let $\widetilde{X}_{M\times N}$ be a rectangular data matrix with independent real-valued entries $[\widetilde{x}_{ij}]$ satisfying $\mathbb {E}\widetilde{x}_{ij}=0$ and $\mathbb {E}\widetilde{x}^2_{ij}=\frac{1}{M}$, $N,M\to\infty$. These entries have a subexponential decay at the tails. We will be working in the regime $N/M=d_N,\lim_{N\to\infty}d_N\neq0,1,\infty$. In this paper we prove the edge universality of correlation matrices ${X}^{\dagger}X$, where the rectangular matrix $X$ (called the standardized matrix) is obtained by normalizing each column of the data matrix $\widetilde{X}$ by its Euclidean norm. Our main result states that asymptotically the $k$-point ($k\geq1$) correlation functions of the extreme eigenvalues (at both edges of the spectrum) of the correlation matrix ${X}^{\dagger}X$ converge to those of the Gaussian correlation matrix, that is, Tracy-Widom law, and, thus, in particular, the largest and the smallest eigenvalues of ${X}^{\dagger}X$ after appropriate centering and rescaling converge to the Tracy-Widom distribution. The asymptotic distribution of extreme eigenvalues of the Gaussian correlation matrix has been worked out only recently. As a corollary of the main result in this paper, we also obtain that the extreme eigenvalues of Gaussian correlation matrices are asymptotically distributed according to the Tracy-Widom law. The proof is based on the comparison of Green functions, but the key obstacle to be surmounted is the strong dependence of the entries of the correlation matrix. We achieve this via a novel argument which involves comparing the moments of product of the entries of the standardized data matrix to those of the raw data matrix. Our proof strategy may be extended for proving the edge universality of other random matrix ensembles with dependent entries and hence is of independent interest.

On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation

AbstractDifferential operators derived from the explicit or implicit solution of a diffusion equation are widely used for modelling background‐error correlations in geophysical applications of variational data assimilation. Key theoretical results underpinning the diffusion method are reviewed. Solutions to the isotropic diffusion problem on both the spherical space \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} and the d‐dimensional Euclidean space \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} are considered first. In \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} the correlation functions implied by explicit diffusion are approximately Gaussian, whereas those implied by implicit diffusion belong to the larger class of Matérn functions which contains the Gaussian function as a limiting case. The Daley length‐scale, defined as \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$D=\sqrt{-\! \left.d/\nabla^{2} c(r)\right|_{r=0}}$ \end{document} where ∇2 is the d‐dimensional Laplacian operator and r = |r| is Euclidean distance, is used as a standard parameter for comparing the different isotropic functions c(r). Diffusion on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} is shown to be well approximated by diffusion on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^2$ \end{document} for length‐scales of interest. As a result, fundamental parameters that define the correlation model on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} can be specified using more convenient expressions available on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^2$ \end{document}.Anisotropic Gaussian or Matérn correlation functions on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} can be represented by a diffusion operator furnished with a symmetric and positive‐definite diffusion tensor. For anisotropic functions c(r), the tensor \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\bf D}=-\! \left( \nabla \nabla^{\rm T} c({\bf r}) |_{{\bf r}={\bf 0}} \right)^{-1}$ \end{document} where ∇ is the d‐dimensional gradient operator, is a natural generalization of the (square of) the Daley length‐scale for characterizing the spatial scales of the function. Relationships between this tensor, which we call the Daley tensor, and the diffusion tensor of the explicit and implicit diffusion operators are established. Methods to estimate the elements of the local Daley tensor from a sample of simulated background errors are presented and compared in an idealized experiment with spatially varying covariance parameters. Since the number of independent parameters needed to specify the local diffusion tensor is of the order of the total number of grid points N, sampling errors are inherently much smaller than those involved in the order N2 estimation problem of the full correlation function. While the correlation models presented in this paper are general, the discussion is slanted to their application to background‐error correlation modelling in ocean data assimilation. Copyright © 2012 Royal Meteorological Society

Sparse Representation Classifier for microaneurysm detection and retinal blood vessel extraction

Diabetic retinopathy (DR) is a common complication of diabetes that damages the retina and leads to sight loss if treated late. In its earliest stage DR can be diagnosed by the presence of a microaneurysm (MA). Although some algorithms have been developed thus far, the accurate detection of MA in a color retinal image is still a challenging problem. By locating a blood vessels’ width, color, reflectivity, tortuosity, and abnormal branching, one can deduce the existence of DR. In this paper we propose new methods to detect MA based on Dictionary Learning (DL) with Sparse Representation Classifier (SRC), and extract retinal blood vessels using SRC. For MA detection we first locate all possible MA candidates with Multi-scale Gaussian Correlation Filtering (MSCF), and then classify these candidates with Dictionary Learning (DL) via SRC. Particularly, two dictionaries one for the MA and one for the non-MA are learned from example MA and non-MA structures, and are used in the SRC process. Experimental results on the ROC database show that the proposed method can well distinguish MA from non-MA objects. Vessel extraction is based on Multi-scale Production of Matched Filter (MPMF) and SRC. First, we locate vessel center-line candidates using Multi-scale Matched Filtering, scale production, double thresholding and center-line detection. Then, the candidates which are center-line pixels are classified using SRC. Two dictionary elements of vessel and non-vessel are used in the SRC process. Experimental results on two public databases show that the proposed method is good at distinguishing vessel from non-vessel objects, and is even able to extract the center-line of small vessels.

Spinal hernia tissue autofluorescence spectrum

The laser intervertebral disc decompression may provide appropriate relief in properly selected patients with contained disc herniations. The present investigation aims to characterise intervertebral disc material by autofluorescence induced by laser light. Degeneration of the intervertebral disc is associated with progressive biochemical changes in disc material. Percutaneous laser disc decompression has become rather popular for the treatment of lumbar disc herniation, but there are problems in the selection of patients. For this purpose, recognition of the disc composition is necessary. We propose a new type of spectroscopic investigation. It is advantageous to the characterization of intervertebral disc material. Intervertebral disc specimens were removed during open surgery from different disc locations. Preoperative patients' MRI was evaluated using the Pfirrmann disc degeneration and Komori scale for migrating of herniated nucleus pulposus. Adjacent slices of stained disc sections were evaluated by histology/histochemistry and autofluorescence spectra. Comparison of the MRI, spectral, histological and histochemical data was performed. The MRI Komori scale correlated with the histology Boos degeneration index. In the histochemistry, collagens other than collagens I and II of the disc were distinguished with best positive correlation coefficient (0.829) and best negative one (-0.904) of proteoglycans of sequester to Boos index. A correlation of the IV Gaussian component of the hernia spectra with the Boos index was established. The Gaussian component correlation with different collagen types and proteoglycan was determined for the disc and sequester. "Autofluorescence-based diagnosis" refers to the evaluation of disc degeneration by histological and histochemical evaluation; it can provide additional data on the degeneration of an intervertebral disc.

Asymptotic Modeling of Coherent Scattering from Random Rough Layers: Application to Road Survey by GPR at Nadir

This paper studies the coherent scattering from random rough layers made up of two uncorrelated random rough surfaces, by considering 2D problems. The results from a rigorous electromagnetic method called PILE (propagation-inside-layer expansion) are used as a reference. Also, two asymptotic analytical approaches are presented and compared to the numerical model for comparison. The cases of surfaces with both Gaussian and exponential correlations are studied. This approach is applied to road survey by GPR at nadir.

Rare, outlier and extreme: beyond the Gaussian model and measures

Probability models for rare, outlier and extreme outcomes are different than the Gaussian (normal) distribution commonly used in management research. This paper illustrates the theoretical basis and implementation of these concepts. One example uses data on organisational size and compensation of CEOs in large US corporations in order to illustrate rare and outlier outcomes. Models that fit the data on these variables are very different than the Gaussian distribution, so mean, standard deviation and correlation are useless here. Another example uses data collected from business executives’ economic forecasts shortly after the 9/11 terrorist attacks to illustrate how to identify extreme outcomes and a Bayesian approach for inferring relationship between extreme outcomes and strategy type. Differentiations between extremes and rares are illustrated using data simulated by a Monte Carlo method. Visualisation of fit of a model for data by Q-Q plot and discussion of distributional testing precedes some concluding remarks.

Statistical Characteristics of Scattered Radiation in Medium With Spatial-temporal Fluctuations of Electron Density and External Magnetic Field

Influence of temporal fluctuations of both electron density and external magnetic field fluctuations on scattered ordinary and extraordinary waves in magnetized plasma is investigated using the ray-(optics) method. Transport equation for frequency fluctuations of scattered radiation has been derived. Broadening of the spatial power spectrum and amplification of the intensity of frequency fluctuation taking into account geometry of the task and the features of turbulent magnetized plasma is analyzed for the anisotropic Gaussian correlation function using the remote sensing data. It is shown that spatial-temporal fluctuations of electron density and external magnetic field, anisotropy and angle of inclination of prolate irregularities relative to the external magnetic field may lead to the exponential amplification of the intensity of frequency fluctuations of scattered electromagnetic waves in the collisional magnetized plasma.

SPATIAL POWER SPECTRUM OF MULTIPLE SCATTERED ORDINARY AND EXTRAORDINARY WAVES IN MAGNETIZED PLASMA WITH ELECTRON DENSITY FLUCTUATIONS

Features of the spatial power spectrum (SPS) of multiple scattered ordinary and extraordinary waves in randomly inhomogeneous magnetized plasma are investigated using the smooth perturbation method taking into account difiraction efiects. Second order statistical moments are derived for arbitrary correlation function of electron density ∞uctuations at oblique illumination of magnetized plasma by mono-directed incident radiation. Numerical calculations have been carried out for anisotropic Gaussian correlation function taking into account anisotropy factor and angle of inclination of prolate irregularities with respect to the external magnetic fleld. It was shown that SPS has a double-peaked shape. External magnetic fleld narrows SPS for ordinary wave and the gap arises in the direction of prolate irregularities. For extraordinary wave the gap increases with a distance passing by the wave in anisotropic magnetized plasma, the width broadens and maximum slightly displaced.