Comparison between ordinary least squares regression and weighted least squares regression in the calibration of metals present in human milk determined by ICP-OES

In this study we compared the use of ordinary least squares and weighted least squares in the calibration of the method for analyzing essential and toxic metals present in human milk by ICP-OES, in order to avoid systematic errors in the measurements used. Human milk samples were provided by maternity clinic Odete Valadares and digested by means of a high-performance microwave (MW) oven. Evaluation of plasma short and long-term stability was made using a solution of digested milk (1:50) with 2.0 mg L⁻¹ Mg in HNO₃ 2% (v/v). The detection power resulted to be at or below the μg L⁻¹ level, whilst the precision expressed as relative standard deviation R.S.D. was almost always equal to or better than 3.3%. Certified reference material Infant Formula (NIST SRM 1846) was used to assess the accuracy of the proposed method, which proved to be accurate and precise. Recovery rates were in the range of 83-117%. Aqueous calibration was carried out for each element under study.     

A tutorial on support vector machine-based methods for classification problems in chemometrics

This tutorial provides a concise overview of support vector machines and different closely related techniques for pattern classification. The tutorial starts with the formulation of support vector machines for classification. The method of least squares support vector machines is explained. Approaches to retrieve a probabilistic interpretation are covered and it is explained how the binary classification techniques can be extended to multi-class methods. Kernel logistic regression, which is closely related to iteratively weighted least squares support vector machines, is discussed. Different practical aspects of these methods are addressed: the issue of feature selection, parameter tuning, unbalanced data sets, model evaluation and statistical comparison. The different concepts are illustrated on three real-life applications in the field of metabolomics, genetics and proteomics.     

A robust and efficient estimation method for single-index varying-coefficient models

A new estimation procedure based on modal regression is proposed for single-index varying-coefficient models. The proposed method achieves better robustness and efficiency than that of Xue and Pang (2013). We establish the asymptotic normalities of proposed estimators and evaluate the performance of the proposed method by a numerical simulation.     

基于高光谱技术检测全蛋粉掺假的研究

传统食品掺假分析多集中于检测特定已知或者怀疑可能存在的掺假物，然而由于掺假形式的多样性以及新的掺假物不断出现，使得传统检测方法具有局限性。目前，全蛋粉作为鲜蛋理想替代品掺假现象十分严重，然而不管是国内还是国外，其掺假检测都鲜有研究。因此，为了探索一种快速检测全蛋粉掺假的方法，研究尝试使用最近快速发展起来的具有绿色、无损等优点的高光谱技术来检测全蛋粉掺假的可行性。从不同地区收集不同品牌的鸡蛋全蛋粉，按不同比例分别掺入淀粉、大豆分离蛋白、麦芽糊精以及三种掺假物的混合物进行试验样品的制备。样品进行光谱采集后，采用ENVI软件选取感兴趣区域(ROI)后提取出平均光谱。根据获得的光谱数据建立全波段下支持向量机(SVM)模型进行掺假的判别并采用偏最小二乘回归(PLSR)模型建立全波段与掺假浓度之间的关系。结果显示，采用径向基核函数所建立的SVM模型，其分类的正确率达到90%以上，基于PLSR建立掺假模型实际值与预测值相关系数R2_P均高于0.90。为了简化模型，采用回归系数法(RC)及连续投影法(SPA)提取特征波长，根据特征波长下的光谱数据建立RC-PLSR和SPA-PLSR模型，结果显示，经简化的模型依然具有良好的性能，说明使用高光谱技术来检测全蛋粉掺假是可行且高效的。     

Adiabatic Potential Energy Surfaces and Photodissociation Mechanisms for Highly Excited States of H2O

Full-dimensional adiabatic potential energy surfaces of the electronic ground state \begin{document}$ \tilde X $\end{document} and nine excited states \begin{document}$ \tilde A $\end{document}, \begin{document}$ \tilde I $\end{document}, \begin{document}$ \tilde B $\end{document}, \begin{document}$ \tilde C $\end{document}, \begin{document}$ \tilde D $\end{document}, \begin{document}$ \tilde D' $\end{document}, \begin{document}$ \tilde D'' $\end{document}, \begin{document}$ \tilde E' $\end{document} and \begin{document}$ \tilde F $\end{document} of H\begin{document}$ _2 $\end{document}O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction. The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials. With a large selected active space and extra diffuse basis set to describe these Rydberg states, the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values. Compared with the well-investigated photodissociation of the first three low-lying states, both theoretical and experimental studies on higher states are still limited. In this work, we focus on all the three channels of the highly excited state, which are directly involved in the vacuum ultraviolet photodissociation of water. In particular, some conical intersections of \begin{document}$ \tilde D $\end{document}-\begin{document}$ \tilde E' $\end{document}, \begin{document}$ \tilde E' $\end{document}-\begin{document}$ \tilde F $\end{document}, \begin{document}$ \tilde A $\end{document}-\begin{document}$ \tilde I $\end{document} and \begin{document}$ \tilde I $\end{document}-\begin{document}$ \tilde C $\end{document} states are clearly illustrated for the first time based on the newly developed potential energy surfaces (PESs). The nonadiabatic dissociation pathways for these excited states are discussed in detail, which may shed light on the photodissociation mechanisms for these highly excited states.     

Data analysis for accelerated life tests via Weibull-gamma frailty regression models

In this article, we study data analysis methods for accelerated life test (ALT) with blocking. Unlike the previous assumption of normal distribution for random block effects, we advocate the use of Weibull regression model with gamma random effects for making statistical inference of ALT data. To estimate the unknown parameters in the proposed model, maximum likelihood estimation and Bayesian estimation methods are provided. We illustrate the proposed methods using real data examples and simulation examples. Numerical results suggest that distribution of random effects has minimal impact on the estimation of fixed effects in the Weibull regression models. Furthermore, to demonstrate the advantage of our proposed model, we also provide methods to compare ALT plans and thus identify the optimal ALT plans.     

The Baeyer‐Villiger oxidation versus aromatic ring hydroxylation: competing organic peracid oxidation mechanisms explored by multivariate modelling of designed multi‐response experiments

Peroxy acids can be used as the terminal oxidant for the Baeyer–Villiger oxidation of acetophenones and for direct ring hydroxylation of methoxy‐substituted benzenes. An oxidative system involving 3‐chloroperbenzoic acid (mCPBA) and 2,6‐dimethoxyacetophenone as model substrate was investigated by means of statistical experimental design, multivariate modelling and response surface methodology. The outcome of the organic peracid oxidation experiments was portrayed by a multi‐response matrix consisting of the yields of three different compounds; 2,6‐dimethoxyphenyl acetate, 1‐(4‐hydroxy‐2,6‐dimethoxy‐phenyl)ethanone and 3‐hydroxy‐2,6‐dimethoxy‐phenyl acetate. The optimized reaction protocol was utilized to investigate a series of various substituted acetophenones. The overall investigation revealed that both the molecular structure of the acetophenone substrate and the experimental conditions exhibited a substantial impact on whether the oxidation reaction follows the oxygen insertion or direct ring hydroxylation mechanism. An improved protocol for the direct ring hydroxylation was also obtained from the experimental and modelling described herein. Copyright © 2015 John Wiley & Sons, Ltd.     

Chemical and mechanical properties of snake fangs

The composition of dental tissues and their interaction determines its mechanical properties. The mechanical properties and chemical composition of the teeth of extant reptiles are still poorly studied areas. As a preliminary study the fangs of four species of snakes and a human tooth were investigated through nanoindentation and Raman spectroscopy. The average elastic modulus values for the main body of the fangs ranged from 15.3 GPa to 24.6 GPa, and 19.1 GPa for the human dentine. Raman spectroscopy and principal component analysis (PCA) showed that snake fangs are similar in composition to human dentine, both of which comprised of hydroxyapatite and an organic matrix. The elastic modulus and hardness data were correlated to the Raman spectra using partial least squares regression (PLS). The spectral features which correlated with the elastic modulus would suggest that elastic modulus is dependent on the relative protein to mineral amounts in the tooth. The form of the phosphate and the relative levels of phosphate to organic components also appear to be governing factors for elastic modulus. The PLS of Raman spectra against the hardness gave very similar results. The small differences between snake fangs and human dentine appeared to be because of carbonate content, with higher levels of carbonate in the human tooth than the snake fangs. Snake fangs should be able to withstand large lateral forces. Human dentine aids in dissipating imposed loads. This similarity in the chemical composition of the snake fangs and human dentine supported the findings of the similarities in mechanical properties, which may be attributed to the similar functional demands of these biocomposites. Copyright © 2016 John Wiley & Sons, Ltd.