Wavelets are explored as a data smoothing (or de-noising) option for solution monitoring data in nuclear safeguards. In wavelet-smoothed data, the Gibbs phenomenon can obscure important data features that may be of interest. This paper compares wavelet smoothing to piecewise linear smoothing and local kernel smoothing, and illustrates that the Haar wavelet basis is effective for reducing the Gi...

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansi...

We consider ®rst the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be approximated by the Green function of a certain linear differential operator. Furthermore, we propose to use the standard (in applied mathematics and engineering) method for asymptotic solution of linear d...

Cortical surface-based analysis of fMRI data has proven to be a useful method with several advantages over 3-dimensional volumetric analyses. Many of the statistical methods used in 3D analyses can be adapted for use with surface-based analyses. Operating within the framework of the FreeSurfer software package, we have implemented a surface-based version of the cluster size exclusion method use...

We consider the Parzen-Rosenblatt kernel density estimate on IP d with data-dependent smoothing factor. Sufficient conditions on the asymptotic behavior of the smoothing factor are given under which the estimate is pointwise consistent almost everywhere for all densities f to be estimated . When the smoothing factor is a function only of the sample size n, it is shown that these conditions are ...

Moo K. Chung , Keith J. Worsley , Jonathan Taylor , Jim Ramsay , Steve Robbins , Alan C. Evans Department of Mathematics and Statistics Montreal Neurological Institute Department of Psychology, McGill University Abstract Gaussian kernel smoothing has been widely used in either 2D flat or 3D volume images, but it does not work on the curved cortical surface. However, by reformulating Gaussian ke...

where f̂ is the classical kernel estimator of the density of X1. This result is striking because it speeds up traditional rates, in root n, derived from the central limit theorem when f̂ = f . Although this paper highlights some applications, we mainly address theoretical issues related to the later result. We derive upper bounds for the rate of convergence in probability. These bounds depend on ...

The lack of consistence and convergence is often considered as a major drawback of smoothed particle hydrodynamics (SPH). Here, we analysis two errors introduced by typical conservative SPH approximations of the gradient of a scalar field: one (smoothing error) is due to smoothing of the gradient by an integration associated with a kernel function; the other (integration error) is due to approx...

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffu...

Almost sure bounds are established for the uniform error of smoothing splines in nonparametric regression with random designs. Some kernel-like properties of the Green’s function for an appropriate boundary value problem are needed to reduce the problem to that for kernel-like regression estimators. Then, results of Einmahl and Mason (2005) imply the required bounds, uniformly in the smoothing ...