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.     

Volumetric behaviour of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system and its binary sub-systems within the temperature range (298.15–328.15) K

Densities and speeds of sound of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system as well as all its binary sub-systems were measured at four temperatures, namely 298.15 K, 308.15 K, 318.15 K, and 328.15 K at atmospheric pressure by a vibrating-tube densimeter DSA 5000. The binary (isooctane + toluene) system was studied previously. Excess quantities (molar volume, adiabatic compressibility, and isobaric thermal expansivity) of the mixtures studied were calculated from the experimental densities and speed of sounds. The excess molar volume data were correlated using the Redlich–Kister equation. Both the positive and S-shaped excess molar volume curves were found for the systems studied. The excess molar volumes versus concentration of binary systems differed in the shape and temperature dependence. The experimental binary data were compared with literature data. The experimental excess molar volumes were analyzed by means of the Extended Real Associated Solution (ERAS) model. The experimental data and the ERAS model can help to estimate real behaviour of the systems studied.     

Gaussian basis sets for molecular applications

The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom‐centered, energy‐optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design. © 2012 Wiley Periodicals, Inc.     

PHI: A powerful new program for the analysis of anisotropic monomeric and exchange‐coupled polynuclear d‐ and f‐block complexes

A new program, PHI, with the ability to calculate the magnetic properties of large spin systems and complex orbitally degenerate systems, such as clusters of d‐block and f‐block ions, is presented. The program can intuitively fit experimental data from multiple sources, such as magnetic and spectroscopic data, simultaneously. PHI is extensively parallelized and can operate under the symmetric multiprocessing, single process multiple data, or GPU paradigms using a threaded, MPI or GPU model, respectively. For a given problem PHI is been shown to be almost 12 times faster than the well‐known program MAGPACK, limited only by available hardware. © 2013 Wiley Periodicals, Inc.     

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc.