Noise and nonlinear estimation with optimal schemes in DTI

In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.     

Near-infrared spectra combined with partial least squares for pH determination of toothpaste of different brands

Near-infrared spectroscopy(NIR),which is generally used for online monitoring of the food analysis and production process, was applied to determine the internal quality of toothpaste samples.It is acknowledged that the spectra can be significantly influenced by non-linearities introduced by light scatter,therefore,four data preprocessing methods,including off-set correction, 1st-derivative,standard normal variate(SNV) and multiplicative scatter correction(MSC),were employed before the date analysis. The multivariate calibration model of partial least squares(PLS) was established and then was used to predict the pH values of the toothpaste samples of different brand.The results showed that the spectral date processed by MSC was the best one for predicting the pH value of the toothpaste samples.     

Efficient robust estimation of time-series regression models

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.     

Spectral/hp penalty least‐squares finite element formulation for unsteady incompressible flows

In this paper, we present spectral/hp penalty least‐squares finite element formulation for the numerical solution of unsteady incompressible Navier–Stokes equations. Pressure is eliminated from Navier–Stokes equations using penalty method, and finite element model is developed in terms of velocity, vorticity and dilatation. High‐order element expansions are used to construct discrete form. Unlike other penalty finite element formulations, equal‐order Gauss integration is used for both viscous and penalty terms of the coefficient matrix. For time integration, space–time decoupled schemes are implemented. Second‐order accuracy of the time integration scheme is established using the method of manufactured solution. Numerical results are presented for impulsively started lid‐driven cavity flow at Reynolds number of 5000 and transient flow over a backward‐facing step. The effect of penalty parameter on the accuracy is investigated thoroughly in this paper and results are presented for a range of penalty parameter. Present formulation produces very accurate results for even very low penalty parameters (10–50). Copyright © 2008 John Wiley & Sons, Ltd.     

Weighted Banzhaf power and interaction indexes through weighted approximations of games

The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considering certain weighted versions of this approximation problem, we define a class of weighted interaction indexes that generalize the Banzhaf interaction index. We show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties. Finally, we give an interpretation of the Banzhaf and Shapley interaction indexes as centers of mass of this subclass of interaction indexes.     

Evaluation of important fatty acid ratios in poultry feed lipids by ATR FTIR spectroscopy

A rapid, simple and reproducible single bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopic method was developed for determination of the n − 6, n − 3 and ratio of n − 6:n − 3 polyunsaturated fatty acids (PUFAs) in poultry feed lipids using partial least squares (PLS) regression. Data for n − 6, n − 3 and ratio of n − 6:n − 3 was acquired by gas chromatography (GC) and used as a standard values for FTIR calibration. The best regression results were achieved using first derivatives of the 1475–650 cm⁻¹ spectral region for n − 6, n − 3 and ratio of n − 6:n − 3 with high regression coefficients (R²) of 0.999, 0.994 and 0.998, respectively and low RMSEP values of 1, 0.06 and 0.83, respectively. The results of the present study revealed that FTIR could be used for rapid and accurate determination of n − 6, n − 3 and ratio of n − 6:n − 3 PUFAs present in poultry feed lipids.     

Noise analysis and suppression method in attitude determination using the global positioning system (GPS)

A noise suppression method is developed for attitude determination using the global positioning system. The influence of noise on attitude determination application is analyzed to determine the relationship of errors. In order to suppress the noise, the total least squares method is utilized for double difference carrier phase measurements and unit vectors between satellites and antennas. Experimental results indicate that compared to the traditional least squares method without noise suppression, the accuracy of the measurement of attitude angles is increased by about 30-50%. The increased computation time of this method does not significantly influence the real time performance for land vehicle application.     

近红外光谱快速测定高浓度烟酰胺

利用烟酰胺在乙醇溶液中波段范围为9001-8060cm^-1和7443-7144cm^-1的近红外一阶导数吸收光谱，经过中心化、矢量归一化预处理，应用偏最小二乘法回归来消除溶剂乙醇的近红外吸收干扰，建立了快速高浓度烟酰胺的方法。54个样本作为校正集，PLS最佳回归因子数为4时，决定系数等于0.997；线性范围为0.13-0.70mol/L。本方法应用于9个待测样品，预测相对偏差小于2.9%，结果令人满意，同时还讨论了一些影响回归精度的因素。     

具有NA误差项的多元回归模型中最小二乘估计的强相合性

在具有NA误差项的多元回归模型中,对误差项和设计矩阵作了一定的限制条件下给出了其最小二乘估计的强相合性;进而得出了NA序列的样本均值的加权和的几乎处处收敛性的结论.     

An omnibus noise filter

A new noise filtering approach, based on flexible least squares (FLS) estimation of an unobserved component local level model, is introduced. The proposed FLS filter has been found to perform well in Monte Carlo analysis, independently of the persistence properties of the data and the size of the signal to noise ratio, ouperforming in general even the Wiener Kolmogorov filter, which, theoretically, is a minimum mean square estimator. Moreover, a key advantage of the proposed filter, relatively to available competitors, is that any persistence property of the data can be handled, without any pretesting, being computationally fast and not demanding, and easy to be implemented as well. This paper was partially written when the author was visiting the Department of Economics at Michigan State University. The author gratefully acknowledges funding from the Fulbright Commission and Michigan State University for hospitality. Many thanks to two anonymous referee and the associate editor for very constructive comments.