素食人群尿液1H NMR代谢轮廓的多因素方差分析

结合方差分析(ANOVA)和偏最小二乘法判别分析(PLS-DA)两种分析技术,对素食和普食人群的尿液1H NMR谱进行分析.利用ANOVA方法将数据矩阵分解为几个独立因素矩阵,滤除干扰因素后,再利用PLS-DA对单因素数据进行建模分析.实验结果表明,ANOVA/PLS-DA方法可以有效地减少饮食因素和性别因素之间的相互...     

食品中合成色素快速检测仪器的研制

基于人工合成色素在可见光区的光吸收及偏最小二乘变量筛选法,研制出合成色素速测仪器,并应用于饮料、糖果、果冻、调色酒等食品中合成色素的快速检测.速测仪具有便携、功耗低、操作简便、检测时间短并可同时对多种人工合成色素进行实时现场快速检测、检测结果准确等优点.对样品中5种食用合成色素柠檬黄、日落黄、胭脂红、苋菜红和亮蓝的检测...     

基于液相色谱-质谱联用技术的代谢组学方法用于中药通心络和人参对过度疲劳大鼠干预作用的评价

用代谢组学方法评价了中药通心络和人参对过度疲劳大鼠的干预作用.通过构造大鼠过度疲劳模型,并分别用通心络和人参进行干预,采用快速液相色谱-离子阱飞行时间质谱(UFLC-IT-TOF-MS)获取大鼠血浆代谢轮廓,并用正交偏最小二乘法(OPLS)进行多变量统计分析,分别找出用于区分通心络和人参干预组大鼠同正常对照大鼠、过度疲...     

Metabolic Profiling of Human Colorectal Cancer Using High Resolution 1H Nuclear Magnetic Resonance Spectroscopy

Colorectal cancer (CRC) is the third commonest malignancy cancer worldwide. Clear understandings of global metabolic profiling of the normal mucosa and cancer tissues are vitally important to aid optimizing the clinical management strategy and understanding CRC biology. We studied metabolic characteristics of 20 CRC and 20 distant normal mucosa tissues extracts from 20 patients using high resolution ¹H NMR spectroscopy in conjunction with multivariate analyses, such as principal component analysis (PCA). Compared with distant normal mucosa tissues, lactate, taurine, ornithine and polyamine were present at significantly higher levels in CRC tissue extracts whereas myo‐inositol was present at significantly lower level. Two metabolites ratios such as myo‐inositol/taurine and myo‐inositol/(ornithine+polyamine) appear to be the most valuable biomarkers for the differentiation CRC from normal mucosa tissues. Our data suggested that HR ¹H NMR spectroscopy combined with multivariate analyses is a potentially useful technology for detecting malignant changes in the normal mucosa tissues, the technique may be further exploited for future CRC biomarker research or identification of targets for therapeutic manipulations.     

Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system

We consider the semiclassical Schrödinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such initial data in the focusing case via the analysis of the compressible Euler-Poisson equations. This example is a large data with radial symmetry, and is beyond the reach of the previous results because the phase part decays too slowly. Extending previous results in this direction, we justify the WKB approximation of the solution with this data for an arbitrarily large interval of R₊.     

Radial symmetry and regularity of solutions for poly-harmonic Dirichlet problems

Let B=B₁(0) be the unit ball in Rn and r=|x|. We study the poly-harmonic Dirichlet problem

     

A system of integral equations on half space

Let be the n-dimensional upper half Euclidean space, and let α be any real number satisfying 0<α<n, we study positive solutions of the following system of integral equations in :

     

Implicitly-weighted total least squares

In a total least squares (TLS) problem, we estimate an optimal set of model parameters X, so that (A-ΔA)X=B-ΔB, where A is the model matrix, B is the observed data, and ΔA and ΔB are corresponding corrections. When B is a single vector, Rao (1997) and Paige and Strakoš (2002) suggested formulating standard least squares problems, for which ΔA=0, and data least squares problems, for which ΔB=0, as weighted and scaled TLS problems. In this work we define an implicitly-weighted TLS formulation (ITLS) that reparameterizes these formulations to make computation easier. We derive asymptotic properties of the estimates as the number of rows in the problem approaches infinity, handling the rank-deficient case as well. We discuss the role of the ratio between the variances of errors in A and B in choosing an appropriate parameter in ITLS. We also propose methods for computing the family of solutions efficiently and for choosing the appropriate solution if the ratio of variances is unknown. We provide experimental results on the usefulness of the ITLS family of solutions.     

Numerical solution of multiple nonlinear Volterra integral equations

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.     

Rational approximation to the Thomas-Fermi equations

We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that Padé approximants of relatively low order are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas-Fermi equation for isolated atoms and for atoms in strong magnetic fields.