Non-negative Matrix Factorization under equality constraints—a study of industrial source identification

This work is devoted to the factorization of an observation matrix into additive factors, respectively a contribution matrix G and a profile matrix F which enable to identify many pollution sources. The search for G and F is achieved through Non-negative Matrix Factorization techniques which alternatively look for the best updates on G and F.These methods are sensitive to noise and initialization, and—as for any blind source separation method—give results up to a scaling factor and a permutation. A Weighted Non-negative Matrix Factorization extension has also been proposed in the literature, so that different standard deviations of the data matrix components are taken into account. However, some estimated profile components may be inconsistent with practical experience. To prevent this issue, we propose an informed Non-negative Matrix Factorization, where some components of the profile matrix are set to zero or to a constant positive value. A special parametrization of the profile matrix is developed in order to freeze some profile components and to let free the other ones.The problem amounts to solve a family of quadratic sub-problems. A Maximization Minimization strategy leads to some global analytical expressions of both factors.These techniques are used to estimate source contributions of airborne particles from both industrial and natural influences. The relevance of the proposed approach is shown on a real dataset.     

Matrix isolation studies of carbonyl selenide,OCSe: Evidence of the formation of dimeric species, (OCSe)2

OCSe isolated in solid Ar or N₂ at 10 K was investigated by FTIR spectroscopy. The IR spectra of OCSe diluted in a 1:1000 proportion with the matrix gases were interpreted in terms of monomeric carbonyl selenide in a single matrix site. The IR spectra of more concentrated matrices revealed several new IR absorptions, which were tentatively assigned to different dimeric structures, aided by the prediction of quantum chemical calculations. The different matrices were exposed to UV–visible broad-band radiation, finding that monomeric OCSe decomposes into CO and Se, as evidenced by the IR absorption of CO perturbed by the presence of a selenium atom in the same matrix cage, while dimeric forms of OCSe decompose giving mainly (CO)₂.     

基于矩阵变换的光场成像及重聚焦模型仿真

基于光场的两平行平面表示方法,针对光场相机两参考平面间的共轴空间距离变换、离轴空间距离变换、轴旋转和沿轴旋转以及透镜作用等对光线描述方式的影响,给出了相应的光场矩阵变换方程,并利用这些方程,建立了光场相机的成像模型、采样模型及辐射传输模型.从光场共轴空间距离变换的观点出发推导出可实现不同点清晰成像的数字重聚焦公式.利用所建立的模型,计算机仿真生成了目标景物,并用所建立模型对生成景物进行了数字重聚焦,验证了数字重聚焦后的图像与直接聚焦图像的一致性.     

Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that $$\|D^{-1}UD\|\ge\|U\|$$ for any matrix norm that is reduced by a pinching. In addition to known examples -weakly unitarily invariant norms - we show that any matrix norm defined by $$\| A \|^{\underline{\underline {{\rm def}}} } \mathop {\max }\limits_{x \ne 0,y \ne 0} {{{\mathop{\rm Re}\nolimits} (x^*Ay)} \over {\phi (x)\psi (y)}},$$ where θ (.) and y (.) are two absolute vector norms, has this property. This includes l p operator norms as a special case.     

Evaluation of matrix effects in the analysis of volatile organic compounds in whole blood with solid‐phase microextraction

The complexity and matrix variability of biological samples requires an accurate evaluation of matrix effects. The dilution of the biological sample is the simplest way to reduce or avoid the matrix effect. In the present study, a set of volatile organic compounds with different volatilities was used to assess the effect of the dilution of blood samples on the extraction efficiency by headspace solid‐phase microextraction. It was found that there was a significant matrix effect but that this effect differs significantly depending on the volatility of the compound. A 1:2 (blood/water) dilution was enough to allow quantitative recoveries of those compounds with boiling points <100°C. For compounds with boiling points between 100 and 150°C, the matrix effect was stronger and a 1:5 dilution was required. The dilution of blood samples proved to be inefficient for quantitative recovery of compounds with boiling points >150°C. A 1:5 dilution of the sample allowed detection limits in the range of nanogram per liter to be obtained. This was sufficient to detect the main volatile compounds present in blood and contamination after exposure.     

An experimental design approach employing artificial neural networks for the determination of potential endocrine disruptors in food using matrix solid-phase dispersion

Matrix solid-phase dispersion (MSPD) as a sample preparation method for the determination of two potential endocrine disruptors, linuron and diuron and their common metabolites, 1-(3,4-dichlorophenyl)-3-methylurea (DCPMU), 1-(3,4-dichlorophenyl) urea (DCPU) and 3,4-dichloroaniline (3,4-DCA) in food commodities has been developed. The influence of the main factors on the extraction process yield was thoroughly evaluated. For that purpose, a 3^(4–1) fractional factorial design in further combination with artificial neural networks (ANNs) was employed. The optimal networks found were afterwards used to identify the optimum region corresponding to the highest average recovery displaying at the same time the lowest standard deviation for all analytes. Under final optimal conditions, potato samples (0.5 g) were mixed and dispersed on the same amount of Florisil. The blend was transferred on a polypropylene cartridge and analytes were eluted using 10 ml of methanol. The extract was concentrated to 50 μl of acetonitrile/water (50:50) and injected in a high performance liquid chromatography coupled to UV–diode array detector system (HPLC/UV–DAD). Recoveries ranging from 55 to 96% and quantification limits between 5.3 and 15.2 ng/g were achieved. The method was also applied to other selected food commodities such as apple, carrot, cereals/wheat flour and orange juice demonstrating very good overall performance.     

悬浮体进样-基体改进效应石墨炉原子吸收光谱法直接测定土壤中的铅和镉

建立了以悬浮体进样-基体改进效应石墨炉原子吸收法测定污灌区土壤中痕量铅和镉的新方法。以琼脂为悬浮剂、NH₄H₂PO₄作基体改进剂,研究了土壤悬浮液的稳定性和基体改进效应及干扰效应。基于原子化峰值时间的对数值与原子化温度之间的线性关系测得Cd和Pb的表观活化能,探讨了基体改进效应机理。应用标准曲线进行校准, Pb和Cd的检出限分别为9.05×10-10 g·mL-1和1.76×10-11 g·mL-1,Pb和Cd的回收率分别为91%～97%和93%～109%,相对标准偏差为4.2%～7.8%。以土壤标准品作参照, 测得值与标准值相符。     

EXPERIMENTAL STUDY OF THE ASYNCHRONOUS MULTISPLITTING RELAXATION METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEMS

We study the numerical behaviours of the relaxed asynchronous multisplitting methods for the linear complementarity problems by solving some typical problems from practical applications on a real multiprocessor system. Numerical results show that the parallel multisplitting relaxation methods always perform much better than the corresponding sequential alternatives, and that the asynchronous multisplitting relaxation methods often outperform their corresponding synchronous counterparts. Moreover, the two-sweep relaxed multisplitting methods have better convergence properties than their corresponding one-sweep relaxed ones in the sense that they have larger convergence domains and faster convergence speeds. Hence, the asynchronous multisplitting unsymmetric relaxation iterations should be the methods of choice for solving the large sparse linear complementarity problems in the parallel computing environments.     

The Nearest Bisymmetric Solutions of Linear Matrix Equations

The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (Ⅰ)A1X1B1 A2X2B2 ^… AkXkBk=D,(Ⅱ)A1XB1 A2XB2 … AkXBk=D and (Ⅲ) (A1XB1,A2XB2,…,AkXBk)=(D1,D2,…,Dk) are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the neaxest solutions axe also provided.