Error estimation in peak‐shape analysis of XPS core‐level spectra using UNIFIT 2003: how significant are the results of peak fits?

An error analysis for numerically evaluating random uncertainties in x‐ray photoelectron spectroscopy has been implemented in version 2003 of the spectra treatment and analysis software UNIFIT in order to improve the understanding of the statistical basis and the reliability of the model parameters for photoelectron spectra. The theoretical basis as well as two approaches to obtain error limits of the fit parameters have been considered. Several test spectra have been analysed and discussed. A representative example has been chosen to demonstrate the relevance of the error estimation for practical surface analysis. Suggestions for the minimization of errors in the peak‐fitting procedures are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Flexible matching of test ligands to a 3D pharmacophore using a molecular superposition force field: Comparison of predicted and experimental conformations of inhibitors of three enzymes

Summary A computer procedure TFIT, which uses a molecular superposition force field to flexibly match test compounds to a 3D pharmacophore, was evaluated to find out whether it could reliably predict the bioactive conformations of flexible ligands. The program superposition force field optimizes the overlap of those atoms of the test ligand and template that are of similar chemical type, by applying an attractive force between atoms of the test ligand and template which are close together and of similar type (hydrogen bonding, charge, hydrophobicity). A procedure involving Monte Carlo torsion perturbations, followed by torsional energy minimization, is used to find conformations of the test ligand which cominimize the internal energy of the ligand and the superposition energy of ligand and template. The procedure was tested by applying it to a series of flexible ligands for which the bioactive conformation was known experimentally. The 15 molecules tested were inhibitors of thermolysin, HIV-1 protease or endothiapepsin for which X-ray structures of the bioactive conformation were available. For each enzyme, one of the molecules served as a template and the others, after being conformationally randomized, were fitted. The fitted conformation was then compared to the known binding geometry. The matching procedure was successful in predicting the bioactive conformations of many of the structures tested. Significant deviation from experimental results was found only for parts of molecules where it was readily apparent that the template did not contain sufficient information to accurately determine the bioactive conformation.     

高空核电磁脉冲模拟波形的双指数函数拟合法

 许多标准和公开出版物中都用双指数函数描述高空核电磁脉冲典型波形。通过数值方法，研究了双指数函数一项重要的性质。根据该性质，详细讨论了高空核电磁脉冲模拟波形数值拟合中，双指数函数特征参数与脉冲峰值、前沿、后沿以及半宽等物理参数的关系，从而提出一种简单有效的脉冲参数计算方法。通过IEC标准中规定的高空核电磁脉冲参数的估计与一个实测高空核电磁脉冲模拟波形的数值拟合，验证了该方法的有效性和可靠性。该方法能够适应多种峰值、前沿和半宽的高宽核电磁脉冲模拟波形的数值拟合。     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

A fitting algorithm for real coefficient polynomial rooting

A new algorithm for computing all roots of polynomials with real coefficients is introduced. The principle behind the new algorithm is a fitting of the convolution of two subsequences onto a given polynomial coefficient sequence. This concept is used in the initial stage of the algorithm for a recursive slicing of a given polynomial into degree-2 subpolynomials from which initial root estimates are computed in closed form. This concept is further used in a post-fitting stage where the initial root estimates are refined to high numerical accuracy. A reduction of absolute root errors by a factor of 100 compared to the famous Companion matrix eigenvalue method based on the unsymmetric QR algorithm is not uncommon. Detailed computer experiments validate our claims.     

基于邻域贡献权值细化的圆心亚像素定位算法

针对传统的圆心算法过程复杂、定位精度受初始边缘提取效果影响较大等问题,提出了一种基于邻域贡献权值细化的圆心亚像素定位算法。首先引入邻域贡献权值系数,改进传统非极大值抑制法,细化边缘;然后在边缘点的梯度方向对灰度值进行高斯拟合,确定亚像素边缘位置;最后针对边缘突变点提出了基于随机抽样一致的最小二乘法来拟合圆心。实验结果表明,该算法具有较好的精度和稳定性,圆心的提取精度可以达到0.1个像素。     

Error evaluation for Zernike polynomials fitting based phase compensation of digital holographic microscopy

Combining the experimental research with the simulation calculation, the error evaluation for Zernike polynomials fitting (ZPF) based phase compensation of digital holographic microscopy (DHM) is performed. The obtained results show that the reconstructed phase with high precision can be obtained by ZPF phase compensation algorithm. Moreover, the phase error for ZPF based phase compensation algorithm increases with both the variation of object height and object transverse area, the larger variation of object height, the larger of phase error, and the larger of object transverse area, the faster increase of RMS phase error. To decrease the error of ZPF phase compensation algorithm, it is required to ensure one of the variations of object height and object transverse area to be a small value. Importantly, the proposed method supplies a useful tool for the error evaluation of phase compensation algorithm.     

参数化连分式拟合方法研究及应用

通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用.     

NMR line‐fitting quantification of polysaccharide N‐acylurea‐based modification in glycoconjugates of Salmonella Typhi Vi polysaccharide

The polysaccharides modification via carbodiimide reaction is one of the most applied methods for obtaining conjugated vaccines against Salmonella enterica. However, N‐acylurea carbodiimide adduct generated in the process is a critical impurity in carbohydrate‐based vaccines. A quantitative NMR method was developed for assessing the N‐acylurea carbodiimide adduct impurity. The procedure was based on line‐fitting facilities for processing the NMR signals on complex spectra. The method showed good linearity, accuracy and precision under inter‐operator variation (relative standard deviation <5%). Copyright © 2017 John Wiley & Sons, Ltd.     

Covariances Simultaneous Component Analysis: a new method within a framework for modeling covariances

In modern omics research, it is more rule than exception that multiple data sets are collected in a study pertaining to the same biological organism. In such cases, it is worthwhile to analyze all data tables simultaneously to arrive at global information of the biological system. This is the area of data fusion or multi‐set analysis, which is a lively research topic in chemometrics, bioinformatics, and biostatistics. Most methods of analyzing such complex data focus on group means, treatment effects, or time courses. There is also information present in the covariances among variables within a group, because this relates directly to individual differences, heterogeneity of responses, and changes of regulation in the biological system. We present a framework for analyzing covariance matrices and a new method that fits nicely in this framework. This new method is based on combining covariance prototypes using simultaneous components and is, therefore, coined Covariances Simultaneous Component Analysis (COVSCA). We present the framework and our new method in mathematical terms, thereby explaining the (dis)similarities of the methods. Systems biology models based on differential equations illustrate the type of variation generated in real‐life biological systems and how this type of variation can be modeled within the framework and with COVSCA. The method is subsequently applied to two real‐life data sets from human and plant metabolomics studies showing biologically meaningful results. Copyright © 2015 John Wiley & Sons, Ltd.