Wolfe步长规则下约束优化问题的共轭梯度投影算法

本文研究了约束优化问题min x∈Ωf(x).利用共轭梯度算法与GLP梯度投影思想相结合的方法,构造了一个新的共轭梯度投影算法,并在Wolfe线搜索下获得了该算法的全局收敛性结果.     

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.     

基于交替投影算法求解单变量线性约束矩阵方程问题

研究如下线性约束矩阵方程求解问题:给定A∈R~(m×n),B∈R~(n×p)和C∈R~(m×p),求矩阵X∈R(?)R~(n×n)"使得A×B=C以及相应的最佳逼近问题,其中集合R为如对称阵,Toeplitz阵等构成的线性子空间,或者对称半(ε)正定阵,(对称)非负阵等构成的闭凸集.给出了在相容条件下求解该问题的交替投影算法及算法收敛性分析.通过大量数值算例说明该算法的可行性和高效性,以及该算法较传统的矩阵形式的Krylov子空间方法(可行前提下)在迭代效率上的明显优势,本文也通过寻求加速技巧进一步提高算法的收敛速度.     

Analysis of the performance of the electric-field-driven liquid crystal lens (ELC Lens) for light of various incident angles

The electric-field-driven liquid crystal lens (ELC) induces the lens effect by the spatially non-uniform distribution of the refractive index. A scheme to analyse the performance of the ELC lens for the lights of various incident angles is devised by the calculation of the phase through the ELC lens and the determination of light ray directions from these phases. The calculated results show that the ELC lens changes the incident light of the plane wave into a focused wave and the focal distance becomes shorter for larger incident angles.     

Direct determination of free bilirubin in serum at sub-nanomolar levels

Direct analysis of free bilirubin in human and animal blood serum samples is reported for the first time. A state-of-the-art system comprised of newly developed high-performance liquid chromatography (HPLC) on reverse-phase (RP) C18 support coupled with thermal lens spectrometric detection (TLS), based on excitation at λ = 457.9 nm by an argon laser was used for this purpose. This HPLC-TLS method enabled a baseline separation of all three structural isomers of bilirubin (XIII-α, IX-α and III-α) and the respective degradation products in isocratic mode in fewer than 7 min. The method excels in ultra-high sensitivity with limit of detection (LOD) and limit of quantitation (LOQ) of 90 pM and 250 pM, respectively. Moreover, this method also affords high precision and accuracy, with correlation coefficients R² > 0.997 over a broad linear range (0.250–150 nM) and R² = 0.9998 in a concentration range of clinical interest (0.500–25 nM). The method's boosted sensitivity enabled to streamline sample preparation to just one serum ultrafiltration step, which made qualitative evaluation of sample preparation possible for the first time. The performance of the HPLC-TLS method was assessed to have 20-fold enhanced sensitivity when compared to a comparable method incorporating HPLC coupled with diode array detector (DAD), which is also a novel method by itself, and could be applied for free bilirubin determination in patients with elevated bilirubin levels.     

Toward the understanding of the environmental effects on core ionizations

Experimental X‐ray absorption spectra are extensively used to determine electronic structure of small molecules but remain difficult to exploit for proteins due to the large number of peaks within their spectra. For such complex systems, theoretical tools like quantum mechanics/molecular mechanics methodology can greatly ease the assignment of the spectra. This study presents a systematic methodology to evaluate core‐ionization energies (E_ion) in proteins with the help of the asymptotic projection approach (Glushkov and Tsaune, Z. Vichislit. Matem. Mat. Fiz. 1985, 25, 298; Glushkov, Chem. Phys. Lett. 1997, 273, 122; Glushkov, Chem. Phys. Lett. 1998, 287, 189; Glushkov, J. Math. Chem. 2002, 31, 91; Glushkov, Opt. Spectrosc. 2002, 93, 15). An in‐depth inspection of E_ion of systems of increasing complexity is considered, going from amino acids to polyglycine and to glycine in human serum albumin (HSA). Computational analysis can help to better understand experimental data and to discriminate environmental effects by tracing them back to individual and collective electrostatic contributions. In the present work, it was found that E_ion of alpha carbon of glycine residues in HSA ranges from 285 to 295 eV depending on their surroundings. © 2014 Wiley Periodicals, Inc.     

核映射和Rank-Order距离的局部保持投影相似性度量方法

针对近红外光谱高维、高冗余、非线性和小样本等特点导致光谱相似性度量时出现的“维度灾难”,提出一种基于核映射和rank-order距离的局部保持投影（KRLPP）算法。首先将光谱数据经过核变换映射到更高维空间,有效保证了流形结构的非线性特征。然后改进局部保持投影(LPP)算法对数据进行降维操作,将rank-order距离替代传统的欧氏距离或测地线距离,通过共享邻近点的信息,得到更加准确的局部邻域关系。最后在低维空间通过距离的计算实现光谱的度量。该方法不仅有效解决了高维空间存在的“距离失效”问题,同时还提高了相似性度量结果的精度。为了验证KRLPP算法的有效性,首先根据降维前后数据集信息残差的变化确定了最佳参数近邻点的个数k和降维后的维数d。其次,从光谱降维投影效果和模型分类效果两个角度与PCA,LPP和INLPP算法进行了对比,结果表明KRLPP算法对于烟叶的部位有较好的区分能力,降维效果以及对于不同部位的正确识别率明显优于PCA,LPP和INLPP。最后,从某品牌卷烟叶组配方中选取了5个代表性烟叶作为目标烟叶,分别采用PCA,LPP和KRLPP方法从300个用于配方维护的烟叶样品中为每个目标烟叶寻找相似烟叶,并从化学成分和感官评价两方面对替换前后的烟叶及叶组配方进行了评价分析。其中LPP和KRLPP用于降维的参数选择保持一致,PCA选择前6个主成分。结果表明,由KRLPP选出的替换烟叶与替换配方在总糖、还原糖、总烟碱、总氮等化学成分以及香气、烟气、口感等感官指标上较PCA、LPP方法差异最小,相似性度量准确度最高。该方法可应用于配方产品替换原料的查找,辅助企业实现产品质量的维护。     

Orlicz Brunn-Minkowski理论

本文主要介绍Orlicz Brunn-Minkowski理论,并从下面3个方面介绍该理论:Orlicz投影体和Orlicz质心体、Orlicz加法与其相关体积不等式、Orlicz Minkowski问题.     

运动背景下的帧间稳像技术

针对运动背景下帧间稳像技术,提出了一种带运动矢量修正的灰度投影运动估计算法。采用该算法分别对当前帧和参考帧的行、列计算灰度投影序列;将当前帧投影序列局部分块,分别将每一分块与参考帧行、列投影曲线进行互相关计算,得到基于局部投影的行、列运动矢量集合;以分块区域的相关置信度为权系数衡量参数,计算每一分块的像素位移权值,从而计算某一方向帧间的加权运动矢量。实验结果表明：该方法可以使运动目标造成的影响只作用于其中若干个局部分块,而其他分块不受此影响,尽可能保证稳像的准确性。采用该方法稳像后的图像与参考帧图像的均方根误差（RMSE）值明显下降,与参考帧图像更加吻合。