Practical alternating least squares for tensor ring decomposition

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional and higher-order data. A well-known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large-scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS-based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR-cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms.     

子孔径拼接检测非球面的初步研究

使用子孔径拼接技术可以无需补偿器、大口径的辅助镜、全息图等辅助元件实现对大口径、大偏离量、高陡度非球面甚至离轴非球面的检验,而且可以同时获得中高频的相位信息,大大地提高了测量精度,降低了成本。在总结了常用检测非球面方法优缺点的基础上提出了利用圆形子孔径、环形子孔径检测非球面的基本原理,并对其步骤的实现、数学模型的建立和拼接算法的开发进行了分析和研究。结果表明,子孔径拼接检测技术可以作为补偿检验以外的另一种定量测试非球面的手段,可以和其它检测方法相互验证,从而确保检测的准确性和可靠性。     

Analytic design of an anamorphic optical system for generating anisotropic partially coherent Gaussian Schell-model beams

The analytic design of anamorphic optical system for transforming the coherent Gaussian beam of a He–Ne laser to a partially coherent Gaussian Schell-model beam with an anisotropic cross-section and an anisotropic degree of coherence is described. Design equations are formulated and some design examples are presented.     

Minimally corrected partial atomic charges for non-covalent electrostatic interactions

We develop a new scheme for determining molecular partial atomic charges (PACs) with external electrostatic potential (ESP) closely mimicking that of the molecule. The PACs are the ‘minimal corrections’ to a reference set of PACs necessary for reproducing exactly the tensor components of the Cartesian zero-, first- and second- molecular electrostatic multipoles. We evaluate the quality of ESP reproduction when ‘minimally correcting’ (MC) Mulliken, Hirshfeld or iterative-Hirshfeld reference PACs. In all these cases, the MC-PACs significantly improve the ESP while preserving the reference PACs’ invariance under the molecular symmetry operations. When iterative-Hirshfeld PACs are used as reference, the MC-PACs yield ESPs of comparable quality to those of the ChElPG charge fitting method.     

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares(IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.     

三维空间二阶精度流体体积界面重构方法

给出三维空间网格模板含81个单元的最小二乘流体体积界面重构方法,并和Youngs方法及网格模板含125个单元的最小二乘流体体积界面重构方法进行比较.静态和动态的测试例子均表明:该方法能精确重构任意方向的平面界面,对C²光滑曲面它能达到二阶收敛精度.和网格模板含125个单元的最小二乘流体体积界面重构方法相比,在达到同样网格精度的条件下,减少了计算量,节省了计算时间,提高了计算效率.     

基于光谱技术的杨梅汁品种快速鉴别方法的研究

为了实现杨梅汁品种的快速无损鉴别,提出了一种用可见和近红外光谱技术快速鉴别杨梅汁品种的新方法。首先采用偏最小二乘法进行模式特征分析,经过交互验证法判别,确定最佳主成分数为9。完成特征提取后,将这9个主成分作为神经网络的输入变量,建立了三层BP神经网络,实现类别预测的同时也完成了数学建模与优化分析工作。3个品种的杨梅汁样本数均为20,共计60个样本。在神经网络学习中,将其分成训练集样本51个和预测集样本9个。对9个未知样本进行预测,准确率为100％。说明本文提出的基于光谱技术和模式识别的方法具有很好的分类和鉴别能力。     

Analysis of a Young–Michelson tandem interferometer

In a Young–Michelson tandem interferometer a Michelson interferometer is illuminated through a pair of Young slits. The pattern produced by this set-up is analyzed theoretically. The consequences of small misalignments and uncompensated arms in the Michelson interferometer are studied. The effects of the spatial and temporal partial coherence of the source are also explored. Experimental results using a laser source are shown to be in good agreement with the predicted theoretical calculations.     

一种面向PX装置成品杂质含量检测的拉曼光谱分析法

面向对二甲苯(PX)成品的在线分析问题,为克服色谱分析法的不足,本文提出了一种基于拉曼光谱的PX成品杂质含量分析方法。为了克服激光中心波长与功率波动带来的不良影响,提出了激光中心波长自动校正与PX特征峰归一化方法;同时,结合相关分析获取了主要杂质的特征波段,并采用偏最小二乘算法进行定量分析。针对11个未知样本,PLS模型对甲苯(MB)、乙苯(EB)、间二甲苯(MX)、邻二甲苯(OX)的标准预测误差分别为0.03%、0.11%、0.02%、0.03%。实验结果表明,拉曼光谱法能够快速、准确且无损地测定PX成品中主要杂质的含量,为在线拉曼分析系统的开发奠定了方法基础。     

基于线性回归算法的春玉米叶面积指数的冠层高光谱反演研究

利用辽宁锦州地区2013年生长季不同土壤水分控制条件下的春玉米冠层高光谱数据,及对应的植株叶面积指数(leaf area index,LAI)数据,分析在不同发育期内不同生长状况下的春玉米冠层高光谱特征及其与植株叶面积指数的关系。采集并计算共313组有效样本,包括350～2 500 nm波段范围光谱的反射率、反射率倒数的对数、反射率一阶导数及LAI,应用多元逐步线性回归法和偏最小二乘回归法,对剔除了受大气水分影响较为严重光谱波段的其他波段数据进行降维,构建叶面积指数的全波段冠层高光谱数据模型,并进行精度检验与比较。结果表明,春玉米LAI与光谱反射率在可见光波段(350～680 nm)、红外波段(1 430～1 800和1 950～2 450 nm)均呈显著的负相关;反射率倒数的对数在对应区间为显著的正相关;反射率一阶导数则在可见光和近红外波段(350～1 350 nm)存在较显著相关波段。三种全波段冠层高光谱数据在春玉米LAI的线性回归中,偏最小二乘法在以冠层反射率为自变量的模型构建中,比多元逐步线性回归拟合度好,其总均方根误差为0.480 7;以冠层光谱反射率的倒数的对数及一阶导数为自变量,应用逐步线性回归法建模,拟合度较好,其总均方根误差分别为0.333 5和0.348 8;三种光谱数据的春玉米LAI两种回归算法中,以冠层反射率倒数的对数为自变量,应用逐步线性回归方法建模的拟合度最佳。