In this paper quasi-random (Halton, Sobol', and Faure) and pseudo-random sequences are compared in computational experiments designed to determine the effects on convergence of certain properties of the integrand, including variance, variation, smoothness, and dimension.
We begin by describing an experimental study where a heuristic optimality criterion gave good tracking performance: the tracking method there was based on maximizing smoothness and overall variation in the drift observer, which was found by solving an eigenvalue problem.
Smoothness of resistivity variation is determined by a model covariance with length scales set to 0.1 as default (see also Additional file6).
The selection of the range intervals is based on the characteristics of human vision's sensitivity to gray value variations from smoothness to contrast.
It should be noted that deconvolution optimization in UDECON is based on the following assumptions (see Shibuya and Michikawa 2000; Jackson et al. 2010; Oda and Xuan 2014): (1) sample magnetization varies only as a function of depth; (2) smoothness of the magnetization variations is similar throughout the sample; and (3) measurement errors follow Gaussian distribution.
Thirdly, one may use different regularization constant λ j for the daily variation pattern γ j pertaining to different road types j to reflect the different levels of smoothness of the daily variation patterns shown in Fig. 1.
The procedure provides a systemic approach for predicting and designing turbomachinery blading reliability against various potential high cycle fatigue problems for all relevant vibratory modes, and taking into account variability in geometry (e.g. dimensional variation, surface smoothness, etc).
Hence, the choice of both the membership functions is suitable as they are best known for representing maximum variation and smoothness.
We impose a local smoothness constraint on the variation of motion vectors by using the energy function, which assigns a smaller probability to the motion vectors that differ significantly from vectors in their spatio-temporal neighbourhood.
For optimization, we employed a combined measure which consists of three evaluation values: CMI, the overlapped region between the extracted 2D MR image and the reference pathological image, and the local smoothness of displacement vector variation.
Optionally, a 'resels per voxel map' can also be generated to record local variations in noise smoothness.
