基于非负分解方法的质谱成像数据特征提取

质谱成像技术能够在同一个实验里无需标记手段而获得样品表面的分子信息及其分布信息,是当前质谱分析的热点.其分析所得数据量大且复杂,使其特征难以提取.多元统计分析方法,特别是主成分分析法已应用于质谱成像数据的压缩和特征提取.然而由于主成分分析常产生负的数据结果,其意义难以解释且不易分解为单一的特征.本研究开发出一种基于非负分解的质谱成像数据提取方法,能够提取单一的分子特征及其在样品上的分布特征,并将多个单一的特征分布通过红、绿、蓝三色叠加显示,获得轮廓直观的综合特征分布.应用本方法对小鼠脑组织切片质谱成像数据进行分析,可直观分解出灰质区域、白质区域和背景区域,相对主成分分析方法更直观且易于解释.应用本方法对在同一个样品靶上的人膀胱癌变组织和其相邻非癌变组织切片质谱成像数据进行分析,癌变与非癌变组织间差异清晰直观.本研究设计的质谱成像软件可由http://www.msimaging.net获取.     

一种基于免疫识别的主因子数判断方法

根据免疫算法的基本思想,提出了一种基于免疫识别(IR)的主因子数判断方法.对模拟数据和HPLC-DAD数据的处理结果表明,IR比嵌入误差(IE)、因子指示函数(IND)和交叉验证(CV)更能有效地克服噪音的影响.当实际数据中的非线性和不等性方差噪音使其它方法失效时,IR仍能得到正确的主因子数.     

主成分分析-支持向量回归建模方法及应用研究

将主成分分析(PCA)用于近红外光谱的特征提取,并与支持向量回归(SVR)相结合,实现了主成分分析-支持向量回归(PCA-SVR)用于近红外光谱定量分析的建模方法。与单纯的SVR方法相比,不仅提高了运算速度,而且提高了模型的预测准确度。将PCA-SVR方法用于烟草样品中总糖和总挥发碱含量的测定,所得结果的预测均方根误差分别为1.323和0.0477;回收率分别为91.8%~112.6%和88.9%~120.2%。     

能量色散X射线散射结合主成分分析对液体易制毒化学品的探测与鉴别分类

采用能量色散X射线散射(EDXRS)技术探测了8种液体易制毒化学品的X射线散射光谱, 结果显示液体易制毒物质具有各自特征的EDXRS散射图谱. 将液体易制毒化学品的EDXRS散射信息与主成分分析结合, 发现前2个主成分可以表达X射线散射光谱的主要信息, 在PC1～PC2得分分布图上可将液体易制毒化学品进行分类. 研究结果表明, EDXRS光谱技术结合主成分分析法可以实现探测、 鉴别分类液体易制毒化学品, 为隐藏液体易制毒化学品的监管控制提供一个可行的鉴别方法.     

Near-monodisperse,n-alkyl,end-functionalized poly(methyl vinyl ether)s: Synthesis by living cationic polymerization and solution characterization

Water-soluble amphiphilic diblock copolymers were synthesized by the living cationic polymerization of methyl vinyl ether (hydrophilic block) and its subsequent termination with n-alcohols of chain lengths varying from one to eight, and three n-alkyl carboxylic acids with 10, 12, and 18 carbon atoms. Additionally, water and ethylene glycol were tested as terminating agents. The extent of the functionalization was determined using ¹H NMR spectroscopy. The cloud points of 1% w/w aqueous solutions of the polymers as determined by turbidimetry decreased from 32 to 21°C as the number of carbon atoms of the terminating agent increased. Aqueous GPC revealed micellization of the stearic acid-terminated block copolymer, while the other block copolymers existed mainly as unimers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. A Polym. Chem. 36: 2547–2554, 1998     

Strong Duality for Proper Efficiency in Vector Optimization

In this paper, we give counterexamples showing that the strong duality results obtained in Refs. 1–5 for several dual problems of multiobjective mathematical programs are false. We provide also the conditions under which correct results can be established.This research was supported by the Brain Korea 21 Project in 2003. The authors thank the referees for valuable remarks.     

On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional χ-eigenspace (with χ a complex ring class character) provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is non-zero. This represents the analogue in the function field setting of a theorem for elliptic curves over Q due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof employs Kolyvagin-type arguments, and the cohomological machinery is started up by the control on the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic.     

Invariant manifolds near a minimizer

A classical result, studied, among others, by Carathéodory [C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989], states that, for second-order, scalar equations, nondegenerate periodic minimizers are hyperbolic. Consequently, the Stable/Unstable Manifold Theorem applies, and implies that, at least locally, the stable and unstable sets are regular curves intersecting transversally at the nondegenerate minimizer.For analytic equations, there is a version of this fact which holds for isolated, but possibly degenerate, minimizers.     

Geometry of cones and an application in the theory of Pareto efficient points

In this article we give a new criterion for the existence of a bounded base for a cone P of a normed space X. Also, if P is closed, we give a partial answer to the problem: is 0 a point of continuity of P if and only if 0 is a denting point of P? The above problems have applications in the theory of Pareto efficient points.     

New Approach to Solving a System of Variational Inequalities and Hierarchical Problems

This paper deals with a viscosity iterative method, in real Hilbert spaces, for solving a system of variational inequalities over the fixed-point sets of possibly discontinuous mappings. Under classical conditions, we prove a strong convergence theorem for our method. The proposed algorithm can be applied for instance to solving variational inequalities in some situations when the projection methods fail. Moreover, the techniques of analysis are novel and provide new tools in designing approximation schemes for combined and bilevel optimization problems.