Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

A useful approach for the differentiation of wines according to geographical origin based on global volatile patterns

In this study, the feasibility of solid‐phase extraction combined with gas chromatography and mass spectrometry in tandem with partial least squares discriminant analysis was evaluated as a useful strategy to differentiate wines according to geographical origin (Azores, Canary and Madeira Islands) and types (white, red and fortified wine) based on their global volatile patterns. For this purpose, 34 monovarietal wines from these three wine grape‐growing regions were investigated, combining the high throughput extraction efficiency of the solid‐phase extraction procedure with the separation and identification ability. The partial least squares discriminant analysis results suggested that Madeira wines could be clearly discriminated from Azores and Canary wines. Madeira wines are mainly characterized by 2‐ethylhexan‐1‐ol, 3,5,5‐trimethylhexan‐1‐ol, ethyl 2‐methylbutanoate, ethyl dl ‐2‐hydroxycaproate, decanoic acid, 3‐methylbutanoic acid, and (E)‐whiskey lactone, whereas 3‐ethoxypropan‐1‐ol, 1‐octen‐3‐ol, (Z)‐3‐hexenyl butanoate, 4‐(methylthio)‐1‐butanol, ethyl 3‐hydroxybutanoate, isoamyl lactate, 4‐methylphenol, γ‐octalactone and 4‐(methylthio)‐1‐butanol, are mainly associated with Azores and Canary wines. The data obtained in this study revealed that solid‐phase extraction combined with gas chromatography and quadrupole mass spectrometry data and partial least squares discriminant analysis provides a suitable tool to discriminate wines, both in terms of geographical origin as well as wine type and vintage.     

An emerging strategy for tracing the anti-erectile dysfunction components of raw and salt-processed semens of Astragali Complanati by combinatory liquid chromatography–mass spectrometry-based quantitative analysis,efficacy assessment on impotent rats,and partial least squares regression

Semens of Astragali Complanati own anti-erectile dysfunction effect; however, the components which contribute to the anti-erectile dysfunction effect remain unclear. This work raised a strategy that integrates liquid chromatography coupled mass spectrometry-based quantitative analysis, anti-erectile dysfunction assessment on impotent rats, and their relationship analysis for pinpointing anti-erectile dysfunction components from semens of Astragali Complanati. For simultaneous quantification of seven major components in raw and salt-processed semens of Astragali Complanati, an accurate and reliable liquid chromatography–mass spectrometry method was developed under multiple reaction monitoring mode. Of note, chloramphenicol was employed as the internal standard. The method showed good linearity and repeatability, where the recovery rates of each component ranged from 98.1 to 104.7%, and the precisions of intra- and interday were all within 3.4%. The method has been used for quantification of the seven major components in 10 batches of raw and salt-processed semens of Astragali Complanati. Then, the anti-erectile dysfunction effects of raw and salt-processed semens of Astragali Complanati were evaluated on impotent rats. Gray relationship analysis and partial least squares regression were combined for elucidating the relationship. As a result, complanatuside, astragalin, complanatoside B, and kaempferol were found to be responsible for anti-erectile dysfunction effect of Astragali Complanati.     

Ultraviolet Spectroscopic Detection of Nitrate and Nitrite in Seawater Simultaneously Based on Partial Least Squares

A direct, reagent-free, ultraviolet spectroscopic method for the simultaneous determination of nitrate (NO₃⁻), nitrite (NO₂⁻), and salinity in seawater is presented. The method is based on measuring the absorption spectra of the raw seawater range of 200–300 nm, combined with partial least squares (PLS) regression for resolving the spectral overlapping of NO₃⁻, NO₂⁻, and sea salt (or salinity). The interference from chromophoric dissolved organic matter (CDOM) UV absorbance was reduced according to its exponential relationship between 275 and 295 nm. The results of the cross-validation of calibration and the prediction sets were used to select the number of factors (4 for NO₃⁻, NO₂⁻, and salinity) and to optimize the wavelength range (215–240 nm) with a 1 nm wavelength interval. The linear relationship between the predicted and the actual values of NO₃⁻, NO₂⁻, salinity, and the recovery of spiked water samples suggest that the proposed PLS model can be a valuable alternative method to the wet chemical methods. Due to its simplicity and fast response, the proposed PLS model can be used as an algorithm for building nitrate and nitrite sensors. The comparison study of PLS and a classic least squares (CLS) model shows both PLS and CLS can give satisfactory results for predicting NO₃⁻ and salinity. However, for NO₂⁻ in some samples, PLS is superior to CLS, which may be due to the interference from unknown substances not included in the CLS algorithm. The proposed method was applied to the analysis of NO₃⁻, NO₂⁻, and salinity in the Changjiang (Yangtze River) estuary water samples and the results are comparable with that determined by the colorimetric Griess assay.     

Discrimination of Beers by Cyclic Voltammetry Using a Single Carbon Screen-printed Electrode

A fast, simple and costless methodology without sample pre-treatment is proposed for the discrimination of beers. It is based on cyclic voltammetry (CV) using commercial carbon screen-printed electrodes (SPCE) and includes a correction of the signals measured with different SPCE units. Data are submitted to partial least squares discriminant analysis (PLS−DA) and support vector machine discriminant analysis (SVM−DA), which allow a reasonable classification of the beers. Also, CV data from beers can be used to predict their alcoholic degree by partial least squares (PLS) and artificial neural networks (ANN). In general, non-linear methods provide better results than linear ones.     

Main Components of Xinjiang Lavender Essential Oil Determined by Partial Least Squares and Near Infrared SpectroscopySCIEI北大核心CSCD

This work was undertaken to establish a quantitative analysis model which can rapid determinate the content of linalool, linalyl acetate of Xinjiang lavender essential oil. Totally 165 lavender essential oil samples were measured by using near infrared absorption spectrum(NIR), after analyzing the near infrared spectral absorption peaks of all samples, lavender essential oil have abundant chemical information and the interference of random noise may be relatively low on the spectral intervals of 7100-4 500 cm(-1). Thus, the PLS models was constructed by using this interval for further analysis. 8 abnormal samples were eliminated. Through the clustering method, 157 lavender essential oil samples were divided into 105 calibration set samples and 52 validation set samples. Gas chromatography mass spectrometry (GC-MS) was used as a tool to determine the content of linalool and linalyl acetate in lavender essential oil. Then the matrix was established with the GC-MS raw data of two compounds in combination with the original NIR data. In order to optimize the model, different pretreatment methods were used to preprocess the raw NIR spectral to contrast the spectral filtering effect, after analysizing the quantitative model results of linalool and linalyl acetate, the root mean square error prediction(RMSEP) of orthogonal signal transformation (OSC) was 0.226, 0.558, spectrally, it was the optimum pretreatment method. In addition, forward interval partial least squares (FiPLS) method was used to exclude the wavelength points which has nothing to do with determination composition or present nonlinear correlation, finally 8 spectral intervals totally 160 wavelength points were obtained as the dataset. Combining the data sets which have optimized by OSC-FiPLS with partial least squares(PLS) to establish a rapid quantitative analysis model for determining the content of linalool and linalyl acetate in Xinjiang lavender essential oil, numbers of hidden variables of two components were 8 in the model. The performance of the model was evaluated according to root mean square error of cross-validation (RMSECV) 9 root mean square error of prediction (RMSEP). In the model, RESECV of linalool and linalyl acetate were 0.170 and 0.416, respectively; RMSEP were 0.188 and 0.364. The results indicated that raw data was pretreated by OSC and FiPLS, the NIR-PLS quantitative analysis model with good robustness, high measurement precision; it could quickly determine the content of linalool and linalyl acetate in lavender essential oil. In addition, the model has a favorable prediction ability. The study also provide a new effective method which could rapid quantitative analysis the major components of Xinjiang lavender essential oil.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015     

Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A_n has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥₂. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.     

一组新氨基酸描述子用于肽定量构效关系研究

用主成分分析从20种天然氨基酸0D～3D结构信息中收集到的共1369个描述子变量得到了一组新氨基酸描述子(SZOTT), 将其用于血管紧张素转化酶抑制剂和苦味二肽结构表征并以偏最小二乘法建立定量构效关系模型, 得复相关系数R_CU²分别为0.894和0.908, 留一法交互检验的复相关系数R_CV²分别为0.828和0.736, 估计均方根误差RMS分别为0.331和0.195. 研究结果表明, SZOTT描述子含信息量大, 操作简便, 结构表达能力强, 有望在多肽定量构效关系研究中得到进一步推广.