A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation

The Poisson‐Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson‐Boltzmann equation. We expose the flux directly through a first‐order system form of the equation. Using this formulation, we propose a system that yields a tractable least‐squares finite element formulation and establish theory to support this approach. The least‐squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Multivariate quality control solved by one‐class partial least squares regression: identification of adulterated peanut oils by mid‐infrared spectroscopy

The Partial least squares class model (PLSCM) was recently proposed for multivariate quality control based on a partial least squares (PLS) regression procedure. This paper presents a case study of quality control of peanut oils based on mid‐infrared (MIR) spectroscopy and class models, focusing mainly on the following aspects: (i) to explain the meanings of PLSCM components and make comparisons between PLSCM and soft independent modeling of class analogy (SIMCA); (ii) to correct the estimation of the original PLSCM confidence interval by considering a nonzero intercept term for center estimation; (iii) to investigate the potential of MIR spectroscopy combined with class models for identifying peanut oils with low doping concentrations of other edible oils. It is demonstrated that PLSCM is actually different from the ordinary PLS procedure, but it estimates the class center and class dispersion in the framework of a latent variable projection model. While SIMCA projects the original variables onto a few dimensions explaining most of the data variances, PLSCM components consider simultaneously the explained variances and the compactness of samples belonging to the same class. The analysis results indicate PLSCM is an intuitive and easy‐to‐use tool to tackle one‐class problems and has comparable performance with SIMCA. The advantages of PLSCM might be attributed to the great success and well‐established foundations of PLS. For PLSCM, the optimization of model complexity and estimation of decision region can be performed as in multivariate calibration routines. Copyright © 2011 John Wiley & Sons, Ltd.     

Simultaneous kinetic spectrophotometric determination of Cu(II), Co(II) and Ni(II) using partial least squares (PLS) regression

A partial least squares (PLS-1) calibration model based on kinetic—spectrophotometric measurement, for the simultaneous determination of Cu(II), Ni(II) and Co(II) ions is described. The method was based on the difference in the rate of the reaction between Co(II), Ni(II) and Cu(II) ions with 1-(2-pyridylazo)2-naphthol in a pH 5.8 buffer solution and in micellar media at 25°C. The absorption kinetic profiles of the solutions were monitored by measuring the absorbance at 570 nm at 2 s intervals during the time range of 0–10 min after initiation of the reaction. The experimental calibration matrix for the partial least squares (PLS-1) model was designed with 30 samples. The cross-validation method was used for selecting the number of factors. The results showed that simultaneous determination could be performed in the range 0.1-2 μg mL⁻¹ for each cation. The proposed method was successfully applied to the simultaneous determination of Cu(II), Ni(II) and Co(II) ions in water and in synthetic alloy samples.      

Ultrasonic and Raman Scattering Spectroscopy of Zinc Thiocyanate Complexes in Water at 25<Superscript>∘</Superscript>C: Kinetics of Complex Formation Determined by Multivariate Analysis

Advances have been made recently in broadening the accessible ultrasonic absorption frequency range and improving the detectability of minor species present in solution using Raman spectroscopy. Development of chemometric techniques in these areas needs to keep pace with the improvement of these experimental methods. Refinements in the analysis of ultrasonic and Raman data based on multivariable least squares and factor analysis, respectively, are examined to investigate the kinetics of zinc thiocyanate complex formation in water. Analysis of ultrasonic absorption relaxation spectra verified that the observed process in aqueous Zn(SCN)₂ involves substitution of water from the first coordination shell of Zn²⁺. Use of a multivariable least-squares error surface is described that enhances the reliability of assigned frequencies of ultrasonic absorption maxima. Factor analysis of Raman scattering data provided direct evidence that at least four complex species, such as Zn(SCN)⁺ and Zn(SCN)₂, are simultaneously present in the aqueous zinc thiocyanate solutions.     

基于逆模型偏最小二乘法的高光谱亚像元目标探测方法研究

目前的高光谱亚像元目标探测算法主要是利用线性混合模型,在背景端元光谱已知的前提下,构造一定的检测算子逐像元判定是否含有亚像元目标。该算法需要较为精确的背景端元光谱先验信息,且目标探测结果受背景复杂度影响较大。从光谱维数据分析的角度出发,将逆模型偏最小二乘法(ILS)和马氏距离奇异值检测方法相结合进行亚像元小目标探测研究。首先建立目标光谱与像元光谱的逆模型,并对像元光谱与目标光谱进行正交变换预处理(SNV),再利用偏最小二乘算法(PLS)计算逆模型的回归系数向量,从而将多维的光谱信息降维,并突出目标光谱信息,最后计算各像元回归系数的马氏距离,判定马氏距离大于3σ的系数所对应的像元点为含有亚像元目标的像元点。该方法仅需要目标光谱的先验信息,对背景的复杂度不敏感。文章采用AVIRIS仿真数据将上述方法与常用的正交子空间投影算法(OSP)的计算结果进行比较,通过比较不同算法的受试者工作特征曲线(ROC)以及信噪比(SNR)变化曲线,证实了该算法具有较快的运算速度和较高的目标探测性能。     

High resolution instrumentation system for fibre-Bragg grating aerospace sensors

A passive technique for high-resolution detection of the wavelength of peak reflection from fibre Bragg grating (FBG) sensors is presented. The approach, based on a de-convolution of the FBG spectrum and the spectrometer resolution, essentially overcomes the low spectral resolution (≈0.1 nm) associated with commercial spectrometers employing CCD detection. The performance of two algorithms, the Centroid Detection algorithm (CDA) and the least squares method (LSQ), are compared. The LSQ algorithm offers resolution enhancement of at least two orders of magnitude and is shown to be independent of the FBG intensity and bandwidth over a broad range.     

正交平衡区组设计统计分析模型参数估计的矩阵表达

正交平衡区组设计(或者广义正交表)是一种类似于正交拉丁方(或者正交表)的新设计,但试验次数大幅减少.定义了一种基于正交相遇平衡区组设计(或者广义正交表)的统计分析模型,根据这个模型,给出了参数的最小二乘估计的矩阵形式.     

Testing for linearity

A nonparametric large sample test is proposed for testing the linearity of a regression model with independent and identically distributed errors satisfying only a very mild tail condition. The statistic is based on the functional least squares estimator of the slope vector. The test is applied to the stack loss data.     

Rapid Classification and Recognition Method of the Species and Chemotypes of Essential Oils by ATR-FTIR Spectroscopy Coupled with Chemometrics

In the present work, the applicability of attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy, coupled with chemometric tools in recognizing essential oils (EOs) for routine control, was evaluated. EOs belonging to Mentha, Cymbopogon, and Lavandula families and to S. rosmarinus and T. vulgaris species were analyzed, and the performance of several untargeted approaches, based on the synergistic combination of ATR-FTIR and Partial Least Squares Discriminant Analysis (PLS-DA), was tested to classify the species and chemotypes. Different spectra pre-processing methods were employed, and the robustness of the built models was tested by means of a Receiver Operating Characteristic (ROC) curve and random permutations test. The application of these approaches revealed fruitful results in terms of sensitivity and specificity, highlighting the potentiality of ATR-FTIR and chemometrics techniques to be used as a sensitive, cost-effective, and rapid tool to differentiate EO samples according to their species and chemotype.     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007