## What is/are Isotropic Gaussian?

Isotropic Gaussian - Stable evaluation algorithms for isotropic Gaussians (Gaussian radial basis functions) have been proposed based on a Chebyshev expansion of the Gaussians by Fornberg, Larsson & Flyer and based on a Mercer expansion with Hermite polynomials by Fasshauer & McCourt.^{[1]}This paper derives central and noncentral limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in R3.

^{[2]}We show that k-means (Lloyd’s algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian mixture models (GMM) with isotropic Gaussians.

^{[3]}The numerical results are compared with those from Euler–Lagrange simulations and two other quadrature-based moment methods, namely, anisotropic Gaussian (AG) and 8-node tensor-product (TP) quadrature.

^{[4]}Numerical calculations are carried out for new spectral function of electron density fluctuations containing both anisotropic Gaussian and power-law spectral functions using the experimental data.

^{[5]}The present work aims at investigating the ability of a Kinetic-Based Moment Method (KBMM) to reproduce the statistics of turbulent particle-laden flows using the Anisotropic Gaussian (AG) closure.

^{[6]}We test these bounds for the case of isotropic Gaussians with equal covariances and whose means are separated by a distance $\eta$, and find (1) that $\gg \log k$ separation suffices to drive the proportion of mismatches of the MLE to 0, and (2) that the expected fraction of mismatched observations goes to zero at rate $O((\log k)^{2}/\eta^{2})$.

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## isotropic gaussian kernel

In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels.^{[1]}The anisotropic edge strength is obtained through the first derivative of anisotropic Gaussian kernels which incorporates an adaptive anisotropy factor.

^{[2]}To better detect edges with heterogeneous widths, in this paper, we propose a multiscale edge detection method based on first-order derivative of anisotropic Gaussian kernels.

^{[3]}The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel.

^{[4]}Using an isotropic Gaussian kernel framework, we show that vector movement is likely to be greater when applying a temporal effect, than when estimated by traditional methods.

^{[5]}In order to design a line detector that minimizes the impact of noise, regardless of the scale or direction of the lines, in this paper, we present a framework for multiscale line detection based on second-order anisotropic Gaussian kernels.

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## isotropic gaussian random

Notice that their result was generalized by Wu and Xiao [Continuity in the Hurst index of the local times of anisotropic gaussian random fields, Stoch.^{[1]}In this paper, we consider the behavior of the maximum likelihood estimators of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function.

^{[2]}Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed.

^{[3]}Let $$X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}$$X={X(t)∈Rd,t∈RN} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions.

^{[4]}A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric.

^{[5]}As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z , while the height distribution remains the same as that of Z.

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## isotropic gaussian model

Using the estimators derived from a simple isotropic Gaussian model of turbulent wind fluctuations, we proposed modified models for estimating the turbulence intensity of wind components.^{[1]}The published results for this landmark data under isotropic Gaussian models and procrustes theory are also discussed.

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## isotropic gaussian distribution

In the reported literature, the measurement error of the image points is usually assumed to obey isotropic Gaussian distribution.^{[1]}In this study, the conventional coplanar relative reachable domain with initial state uncertainty in isotropic Gaussian distribution is extended to the three-dimensional case with uncertainty in arbitrary Gaussian distribution.

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## isotropic gaussian microturbulence

The standard concept of isotropic Gaussian microturbulence was assumed in this study.^{[1]}The standard concept of isotropic Gaussian microturbulence was assumed in this study.

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