基于新型分子距边矢量ν与多元统计方法对于烷烃13C NMR化学位移和(CSS)估计与预测的深入研究

基于本实验室提出一种新型以势能形式表达的分子距边矢量, 深入地系统研究了核磁共振碳-13谱化学位移和(CSS)规律以及分子拓扑指数矢量在定量结构波谱关系(QSSR)中的应用. 借助多种计量化学方法包括多元线性回归、逐步多元回归、主成分回归、主筛选回归等进行分子拟模和定量相关研究, 发现烷烃¹³C NMR 化学位移和(CSS)与其分子距边矢量及路径长度指数有良好线性相关性, 回归方程及其统计参数为:CSS=bν+cp₃=∑_^mj=0b_jν_j+b₁₁p₃=b₀ν+b₁ν₁+b₂ν₂+b₃ν₃+b₄ν₄+b₅ν₅+b₆ν₆+b₇ν₇+b₈ν₈+b₉ν₉+b₁₀ν₁₀+b₁₁p₃=-13.576+22.179ν₁+28.407ν₂+25 .950ν₃+26.690ν₄+14.498ν₅+5.726ν₆-5.379ν₇-3.214ν₈-15.021ν₉ -25.710ν₁₀+12.278p₃ n=63, R=0.997, EV=99.68%, RMS=3.7348, SD=4.1 18, F= 773.116, U=144228.844, Q=864.938; CV: R²_CV=0.980, EV=98.83%, RMS=7.126 1, SD_CV=7.634, F_CV=221.720, U_CV=142121.891, Q_CV=2971 .896.结果良好.     

基于多元局部多项式方法的混沌时间序列预测

根据Takens定理，把混沌时间序列构造为一组序列对，然后用多元局部多项式方法来预测其序列.这种核估计方法可以结合局域法与全局法的优点，使得预测的精度更高.仿真结果表明，该方法非常有效.     

Determination of the refractive index of spherical erythrocytes of human blood in the range 0.3–1.2 µm

A proposed procedure for determining the spectral values of the refractive index of spherical erythrocytes of human blood is based on angular light scattering and the use (for one-time scattering) of a multiple regression equation. A theoretical study of the stability of the relationship between the light scattering indicatrix and the refractive index of erythrocytes toward possible variations of their microstructure parameters is performed in order to select the optimal angles. The precision of the proposed method and its sensitivity to indicatrix measurement uncertainties are estimated. __________ Translated from Zhurnal Prikladnoi Spektroskopii Vol. 74, No. 3, pp. 382–386, May–June, 2007.     

Low silicon non-grain-oriented electrical steel: Linking magnetic properties with metallurgical factors

Commercial supply, from several steel manufacturers, of low-silicon non-grain-oriented electrical steel was monitored over a span of several years. A total of 51 samples were selected—selected from many hundreds on the basis of large differences in magnetic properties, but absence of significant variations in chemistry (other than differences in silicon percentage). The selected samples were analyzed for crystallographic texture and for grain size.     

ERM learning with unbounded sampling

The learning approach of empirical risk minimization (ERM) is taken for the regression problem in the least square framework. A standard assumption for the error analysis in the literature is the uniform boundedness of the output sampling process. In this paper we abandon this boundedness assumption and conduct error analysis for the ERM learning algorithm with unbounded sampling processes satisfying an increment condition for the moments of the output. The key novelty of our analysis is a covering number argument for estimating the sample error.     

A regression approach to ROC surface, with applications to Alzheimer’s disease

We consider the estimation of three-dimensional ROC surfaces for continuous tests given covariates.Three way ROC analysis is important in our motivating example where patients with Alzheimer’s disease are usually classified into three categories and should receive different category-specific medical treatment.There has been no discussion on how covariates affect the three way ROC analysis.We propose a regression framework induced from the relationship between test results and covariates.We consider several practical cases and the corresponding inference procedures.Simulations are conducted to validate our methodology.The application on the motivating example illustrates clearly the age and sex effects on the accuracy for Mini-Mental State Examination of Alzheimer’s disease.     

Asymptotics of the regression quantile basic solution under misspecification

We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed. The research for this paper was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Algorithmic inference: From information granules to subtending functions

To get a true hybrid framework for taking operational decisions from data, we extend the Algorithmic Inference approach to the Granular Computing paradigm. The key idea is that whether or not we need to make decisions instead of mere computations depends on the fact that collected data are not sufficiently definite; rather, they are representative of whole sets of data that could be virtually observed, and we need to manage this indeterminacy. The distinguishing feature is that we face indeterminacy exactly where it affects the quality of the decision. This gives rise to a family of inference algorithms which can be tailored to many specific decisional problems that are generally solved only in approximate ways. In the paper we discuss the bases of the paradigm and provide some examples of its implementation.     

一种新的拓扑指数用于手性化合物的构效关系研究

为了研究羟酸类和氨基酸类手性化合物的构效关系,本实验引进了手性乘积算法:P＝(1-b/a)(1-c/b)(1-a/c)(1-a/d),其中a、b、c和d分别为与分子中手性中心碳原子4个不同连接片断手性eAm指数和分子连接性指数mx的计算值,并考察了所得参数与羟酸类和氨基酸类化合物手性薄层色谱保留指数的相关性.为了评定所得预测模型的稳定性,文中运用了交叉验证法.结果表明,由人工神经网络方法(BP法)所得数学模型比较稳定,且明显优于多元回归分析结果.