一个拟极小化左共轭梯度算法及其数值表现

左共轭梯度法是求解大型稀疏线性方程组的一种新兴的Krylov子空间方法.为克服该算法数值表现不稳定、迭代中断的缺点,本文对原方法进行等价变形,得到左共轭梯度方向的另一迭代格式,给出一个拟极小化左共轭梯度算法.数值结果证实了该变形算法与原算法的相关性.     

铬过渡层位置及金属沉积角度对纳米球刻蚀法制备二维银纳米点阵结构的影响

利用纳米球刻蚀法制备了二维六角密排三角形银纳米阵列, 通过加入铬过渡层并改变其位置和改变金属沉积角度, 研究它们对点阵结构的影响. 实验发现, 加入铬过渡层所形成的银纳米点阵结构较无铬层有很大改善, 三角形角部更加尖锐, 更能满足传感器对信号检测的要求. 同时, 该过渡层应蒸镀在模板球排列之后, 才能获取更大面积的二维银纳米点阵结构. 在沉积角度对制备二维银纳米点阵的实验中, 基片没有旋转, 采用垂直镀膜方式更容易得到结构完整、结合较牢固、且面积较大、角部尖锐的二维银纳米点阵. 吸收光谱测量进一步验证了铬过渡层对二维银纳米点阵形貌结构的改善作用. 这些为下一步的生物修饰以及生物化学传感器的制备提供了先决条件.     

基于分布式光纤Bragg光栅传感技术的光缆卷盘静态压力研究

基于对光缆卷盘缆层静态压力分布的理论分析, 建立了光缆缠绕体系中的受力理论模型. 研究表明, 随着缠绕层数的增加, 卷盘各层光缆所受压强先快速增大而后变化平缓. 采用分布式光纤Bragg光栅(FBG)对光缆绕线装置上缆层的静态压力进行了实时传感, 理论上给出了FBG的中心波长偏移量与体系压强的定量关系, 实验上发现各层FBG的中心波长随着光缆卷盘缠绕层数的增加先较快速变化而后趋于平缓, 理论模拟和实验测量结果符合得很好. 该技术解决了光缆绕线过程中无法对缆层所受压力进行实时监测的难题.     

Geometric detection of coupling directions by means of inter-system recurrence networks

We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K>2$K>2$ coupled subsystems.     

由校正矩阵的等内积分解矩阵确定搜索方向的拟牛顿算法

把正定矩阵关于向量的等内积分解算法应用于求解无约束优化问题的拟牛顿算法中,提出了利用校正矩阵的等内积分解矩阵确定搜索方向的一种新算法和等价于DFP和BFGS校正公式的新的迭代公式.     

Multi-view side information-incorporated tensor completion

Tensor completion originates in numerous applications where data utilized are of high dimensions and gathered from multiple sources or views. Existing methods merely incorporate the structure information, ignoring the fact that ubiquitous side information may be beneficial to estimate the missing entries from a partially observed tensor. Inspired by this, we formulate a sparse and low-rank tensor completion model named SLRMV. The ${\ell }_0$-norm instead of its relaxation is used in the objective function to constrain the sparseness of noise. The CP decomposition is used to decompose the high-quality tensor, based on which the combination of Schatten $p$-norm on each latent factor matrix is employed to characterize the low-rank tensor structure with high computation efficiency. Diverse similarity matrices for the same factor matrix are regarded as multi-view side information for guiding the tensor completion task. Although SLRMV is a nonconvex and discontinuous problem, the optimality analysis in terms of Karush-Kuhn-Tucker (KKT) conditions is accordingly proposed, based on which a hard-thresholding based alternating direction method of multipliers (HT-ADMM) is designed. Extensive experiments remarkably demonstrate the efficiency of SLRMV in tensor completion.