旋转微扰法用于确定化学体系的组分数

本文提出了一个新的用于估计化学体系组分的化学计量学方法,方法的基础在于具有化学意义的特征子空间对微扰和数据的旋转变换具有较大的稳定性,通过观察多次实验中投影残差的标准方差来确定化学秩。对实际化学体系的分析结果表明,该法为组分数的估计提供了一个有价值的工具。     

化学演讲过程数据的自动分辨: 复杂石油样品的GC－MS分析

基于几种新化学计量学方法,提出了可自动解析化学演进数据的新途径。在该法中,首先选择关键向量。通过子空间比较法确定数据的化学秩。以关键向量为起点,通过初等变换不断迭代而实现对数据的解析。并利用数据非负性等检验解析结果的可靠程度。结合GC－MS数据的特点,选择的关键变量可为关键质谱或关键浓度曲线。该方法能极大地减少人为干预,大大降低数据分析时间,对文中的石油样本共解析出557个成分。     

化学演讲过程数据的自动分辨: 复杂石油样品的GC－MS分析

基于几种新化学计量学方法,提出了可自动解析化学演进数据的新途径。在该法中,首先选择关键向量。通过子空间比较法确定数据的化学秩。以关键向量为起点,通过初等变换不断迭代而实现对数据的解析。并利用数据非负性等检验解析结果的可靠程度。结合GC－MS数据的特点,选择的关键变量可为关键质谱或关键浓度曲线。该方法能极大地减少人为干预,大大降低数据分析时间,对文中的石油样本共解析出557个成分。     

色谱数据可视化及天然植物药指纹特征发现方法

提出一类色谱分析数据可视化方法,并用于发现天然植物药的化学指纹特征。选取中药材川芎作为典型研究对象,采用核主成分分析和空间投影变换法对色谱分析数据进行预处理,提取特征信息,再利用二维灰度映像对变换后的数据进行可视化表达,发现其化学指纹特征,从而直接反映出药材质量类别间的化学模式差异。将该方法用于辨识34个不同产地及等级的川芎样品,结果令人满意,证明其具有视觉模式分辨优点,是表达隐含特征指纹和辨识复杂化学物质体系的有力工具。     

利用减秩因子分析法同时优化确定化学反应级数和速率常数

通过对反应过程中在线测得的动力学谱-光谱二维数据矩阵进行主成分分析，可确定化学反应过程存在的组分数。提出用优化动力学参数-减秩因子分析法解析二维数据矩阵，对未知动力学模型的复杂反应可同时优化求解第一步反应的级数和速率常数。模拟二维数据验证了该方法的可行性。该方法用于高锰酸钾氧化溴化钠的反应过程中测得的二维数据的解析，结果表明：高锰酸钾的还原过程符合0级反应模型。     

复杂化学体系测量数据的主因子数估计方法的分类及进展

复杂化学体系的数据解析中,估计主因子数是必要步骤,同时也是一个难题.目前存在多种各具特点的估计方法.对这些方法进行整理和归纳可为解决这一难题提供全局视角下的综合性信息,有助于进一步研究.本文结合本课题组的相关研究对主因子数估计问题进行了系统深入的分析;整理了近年来出现的各种估计方法,并将之分为三类,即经验方法、数学原理完备的方法以及统计方法,并对每类方法的特点和共性进行了分析和说明;归纳出第二类方法的基本原理.     

分析化学计量学的若干新进展

对分析化学计量学的若干新进展进行了讨论, 侧重从作者实验室所进行的研究工作的视角论述了高维数据的分辨、用于化学信号处理的形态学理论和方法、解决复杂化学问题的多元校正和化学模式识别以及联用色谱仪二维数据的分辨新方法的发展.     

速率常数-秩分析法在化学反应过程分析中的应用

针对化学反应动力学谱-吸收光谱组成的两维数据,提出了以优化速率常数而消去反应物波谱信息为减秩手段的速率常数-秩分析法(RCRA).结果表明,RCRA在一次优化过程中可同时获得两个最优解,分别对应于两步速率常数.在获得动力学参数的前提下,利用最小二乘回归可解出包括中间体在内的各组分的吸收光谱.该方法用于处理苯胺电解降解的两维数据,发现苯胺降解过程中有一种表观中间体存在,降解过程符合一级连串反应模型.     

二维小波变换与子窗口因子分析法结合用于含噪声HPLC-DAD数据的解析

将二维小波变换与子窗口因子分析法相结合,用于模拟的高噪声HPLC-DAD数据的解析.首先应用二维小波变换滤除噪声,然后采用子窗口因子分析法解析重叠峰.结果表明,信噪比为10的高噪声基本被滤除掉.     

动力学体系二维数据的秩分析及其应用

详细论证了动力学体系中存在的多种共线性情况,以及在此情况下二维数据阵的秩与独立反应数及组分数的关系.分析了通过增秩这一方式来判断体系组分数的条件.讨论了反应间存在物质交换对数据阵秩的影响.建立起一套通过秩分析判断未知动力学体系中存在的反应组分数、独立反应数以及可能反应机理的方法.将秩分析技术应用到聚苯胺与质子酸反应,初步分析了该体系存在的多种吸光性结构及结构变化.确定了[H＋]=0.01～0.1 mol•L－1范围内,聚苯胺与质子酸反应存在一个三结构两步互变过程.     

Estimating the chemical rank of three-way data arrays by a simple linear transform incorporating Monte Carlo simulation

Estimating an appropriate chemical rank of a three-way data array is very important to second-order calibration. In this paper, a simple linear transform incorporating Monte Carlo simulation approach (LTMC) to estimate the chemical rank of a three-way data array was suggested. The new method determines the chemical rank through performing a simple linear transform procedure on the original cube matrix to produce two subspaces by singular value decomposition. One of two subspaces is derived from the original three-way data array itself and the other is derived from a new three-way data array produced by the linear transformation of the original one. Projection technique incorporating the Monte Carlo approach acts as distinguishing criterion to choose the appropriate component number of the system. Simulated three-way trilinear data arrays with different noise types (homoscedastic and heteroscedastic), various noise level as well as high collinearity are used to illustrate the feasibility of the new method. The results have shown that the new method could yield accurate results with different conditions appended. The feasibility of the new method is also confirmed by two real arrays, HPLC-DAD data and excitation-emission fluorescent data. All the results are compared with the other three factor-determining methods: factor indicator function (IND), core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approach. It shows that the newly proposed algorithm can objectively and quickly determine the chemical rank to fit the trilinear model.     

A novel efficient way to estimate the chemical rank of high-way data arrays

A novel method, a subspace projection of pseudo high-way data array (SPPH), was developed for estimating the chemical rank of high-way data arrays. The proposed method determines the chemical rank through performing singular value decomposition (SVD) on the slice matrices of original high-way data array to produce a pseudo high-way data array and employing the idea of the difference of the original truncated data set and the pseudo one. Compared with traditional methods, it uses the information from eigenvectors combined with the projection residual to estimate the rank of the three-way data arrays instead of using the eigenvalue. In order to demonstrate the excellent performance of the new method, simulated and real three-way data arrays were carried out by the proposed method. The results showed that the proposed method could accurately and quickly determine the chemical rank to fit the trilinear model. Moreover, the newly proposed method was compared with the other four factor-determining methods, i.e. factor indicator function (IND), ADD-ONE-UP, core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approaches. It was found that the proposed method can deal with more complex situations with existence of severe collinearity and trace concentration than many other methods can and performs well in practical applications.     

Use of pseudo-sample extraction and the projection technique to estimate the chemical rank of three-way data arrays

Determining the rank of a trilinear data array is a first step in subsequent trilinear component decomposition. Different from estimating the rank of bilinear data, it is more difficult to decide the significant number of component to fit the trilinear decompositions exactly. General methods of rank estimation utilize the information contained in the singular values but ignore information from eigenvectors. In this paper, a rank estimating method specifically for trilinear data arrays is proposed. It uses the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo sample matrices which are then decomposed by singular value decomposition. Two eigenvectors combined with the projection technique are used to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noise, different noise levels, high collinearity, and real three-way data arrays have been used to illustrate the feasibility of the proposed method. Compared with other factor-determining methods, for example use of the factor indication function (IND), residual percentage variance (RPV), and the two-mode subspace comparison approach (TMSC), the results showed that the new method can give more reliable answers under the different conditions applied.      

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called “SANAS” and “SARAF.” In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.     

Evaluation of variation matrix arrays by parallel factor analysis

PARAFAC is one of the most widely used algorithms for trilinear decomposition. The uniqueness properties of the PARAFAC model are very attractive regardless of whether one is interested curve resolution or not. The fact that PARAFAC provides one unique solution simplifies interpretation of the model. But in three‐way data arrays the uniqueness condition can only be expected when k_A + k_B + k_C ≥ 2F + 2, where F is the number of components and k's are the Kruskal ranks of loadings A to C. As much as second order instruments produce data of varying complexity depending upon the nature of the analytical techniques being combined, with some three‐way data it is possible for patterns generated by the underlying sources of variation to have sufficient independent effects in two modes, yet nonetheless be proportional in a third mode. For example, in three‐way data for spectrophotometric titrations of weak acids or bases (pH‐wavelength‐sample), a rank deficiency may occur in two modes, that is closure rank deficiency in the pH mode and proportionality rank deficiency in the sample direction because each analyte will have acidic and basic forms that are linear combinations in the sample mode. The goal of the present paper is to overcome the non‐uniqueness problem in the second order calibration of monoprotic acids mixtures. The solution contains two steps: first each pH‐absorbance matrix is pretreated by subtraction of the first spectrum from each spectrum in the data matrix. This pretreated data matrix is called the variation matrix. Second, by stacking the variation matrices, a three‐way trilinear variation data array will be obtained without the proportional linear dependency problem that can be resolved uniquely by PARAFAC. It is shown, although unique results are not guaranteed by the Kruscal's condition for the original three‐way data, this condition is fulfilled for pretreated three‐way data. Hence, the variation array may be uniquely decomposed by the PARAFAC algorithm. Studies on simulated as well as real data array reveal the applicability of the proposed method to this kind of problem in the second order calibration of monoprotic acids. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal non-linear dimension reduction scheme for classical molecular dynamics

The optimal creation of a reduced space that effectively captures the long timescale dynamics of a non-linear molecular system over a range of frequencies is described. The technique builds on a previously developed subspace method based on linear constant projective transformation of the original full space. The present work attempts to propose transformation that are spatially dependent thereby leading to an effective subspace for better representing the dynamics of interests. The algorithm seeks out an optimal transformation consistent with desired low frequency motion in a rather general way. The method is demonstrated for a six-dimensional nonlinear system reduced to two-dimensions. Superior performance is found in evaluating ensemble-averaged classical dynamical properties.     

Note on the Error Analysis of the Generalized Rankannihilation Method

ABSTRACT

The generalized rank annihilation method (GRAM) is a method for curveresolution and quantitation that uses two data matrices simultaneously, i.e., onefor the unknown and one for the calibration sample. Requirements have beenderived that ensure the unique resolution of the analyte of interest in thepresence of unknown interferences if the data matrices are free fromexperimental error. In this paper, it is shown that the same requirements allowfor correct determination of bias and variance in the quantitative results obtainedby GRAM if the data matrices are not free from experimental error.     

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

In this work rank annihilation factor analysis (RAFA) is used to analyze difference spectra of kinetic‐spectrophotometric data. Annihilation of the contribution of one chemical component from the original data matrix is a general method in RAFA. However, sometimes RAFA is not suitable for studying rank deficient data such as kinetic‐spectrophotometric measurements. On the other hand, in order to apply RAFA for the determination of an analyte in an unknown sample, a standard two‐way matrix of the analyte with rank one should generally be available. This is not usually attainable for kinetic‐spectrophotometric monitoring of complexation reactions. Processes monitored by difference spectroscopy always have the spectrum of the initial stage subtracted from each spectrum in the data matrix. In this work we show that, for kinetic‐spectrophotometric data of complexation reactions, the spectrum of ligand (reactant) itself can be used as initial spectrum for subtraction. The obtained difference matrix of sample and that of analyte of interest will be full‐rank and rank 1, respectively. Therefore the system can be analyzed by RAFA. The proposed method was investigated with simulated data at the first stage. The method was then applied in the analysis of experimental kinetic‐spectrophotometric data of a complexation reactions of Co(II) and Ni(II) with chromogenic reagent 1‐(2‐pyridylazo) 2‐naphthol in order to do multi‐component determination of these ions in various real samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of perturbative and variational treatments of molecular vibrations: application to the vibrational spectrum of HFCO up to 8000 cm(-1)

We calculated highly excited states of the HFCO molecule, comparing results from two methods. In the first method, Van Vleck perturbation theory is used to transform away all off-diagonal couplings except those between nearly degenerate states. This perturbative transformation leads to a matrix representation where eigenvalues are obtained with relatively small matrices. In the second method, variational eigenvalues are obtained by combining the Jacobi-Wilson approach with the block-Davidson scheme. The key ingredient here is a prediagonalized-perturbative scheme applied to a subspace of a curvilinear normal-mode basis set. Comparisons of the two methods provide a critical test of the less time-consuming perturbation theory. Two different coordinate sets are used to test the sensitivity of the results to coordinate choice. Perturbation theory also requires a polynomial fit to the potential. The implications of this restriction are investigated.