Using the Tsallis distribution and the fractional differentiation to resolve the overlapping bands

Using the Tsallis distribution, which facilitates the generalization of well-known distributions such as Gaussian and Lorentzian by varying a non-extensivity parameter q as a model of the individual band to correctly assign overlapping bands and the fractional differentiation as mathematical tool to help to determine the spectral parameters of the individual band, a new resolution method for the overlapping bands is presented. According to variation of the maximum and the zero-crossing of the Tsallis distribution at different differential order, two types of parameter estimators are obtained, which are utilized to calculate the parameters of position, height, and width of Tsallis distribution. To verify the suggested method, separation of several kinds of overlapping bands simulated by computer and the experimental infrared spectrum of 1,2-bromofluoroethane have been performed and discussed. Figure α-Order differentiation of the overlapping band     

A New Method to Resolve Overlapped Voltammetric Peaks

A new method called spline convolution (SC) for resolving overlapped peaks was proposed in this paper. The differential pulse voltammetric overlapped peaks of mixtures of Pb(Ⅱ） and T1(I) were investigated by this method, and satisfactory results were obtained. The results show excellent correlation between peak areas of the processed signals and the concentrations.     

基于积分渐进展开的气相色谱重叠峰快速解析法

论文提出用积分渐进展开解析气相色谱重叠峰,该方法有3个主要步骤：首先将谷峰或肩峰分成两个积分区域,得到一个子区域的积分方程和一个重叠峰面积的代数方程;然后用数值积分求出这两个方程计算中所需要的峰面积,再用积分渐进公式将积分方程展开成代数方程;最后,将这两个方程与峰高约束方程联立后,得到一个非线性代数方程组,用Gauss-Seidel迭代可以快速求解方程组,方程收敛的最大迭代次数不超过20次。仿真和实验结果表明,解析的峰高和峰面积误差均很小,峰面积最大误差低于6.44%,峰高的最大误差约为6.80%。由于该算法精度高,效率高,所以这个方法可以用于气相色谱重叠峰和一般色谱峰的实时在线解析。     

Spline wavelet in the resolution of overlapping voltammetric peaks

Spline wavelet transform is used to resolve overlapping voltammetric peaks. A suitable resolving factor is chosen to multiply the filters of spline wavelet and make it a peak resoluter. Simulated overlapping voltammetric peaks are processed by the peak resoluter and satisfactory results are obtained. Base-line separation can be achieved, the relative errors of peak position are less than 3.0%, and the relative errors of peak area are less than 5.0%. The effect of different resolving factors and spline wavelet basis are discussed. To test the procedure, two systems, cadmium (Ⅱ)-indium (Ⅲ) and lead (Ⅱ)-thallium (Ⅰ), are used.     

小波变换用于植物激素重叠色谱峰中组分的定量分析

根据小波变换将信号按频率大小分解的性质，作者提出了一种用小波变换直接提取重叠色谱峰中单一组分信息的方法，并将其应用于植物激素混和体系重叠峰的解析与定量分析。结果表明：单组分的色谱信号经小波变换分解后仍能保持原有的线性关系，用小波变换从重叠信号中提取的单一组分信息也具有良好的线性关系。     

H-point standard additions method for resolution of overlapped chromatographic peaks with a conventional fluorescence detector. Determination of phenol and cresols in waters

Summary The H-Point Standard Additions Method (HPSAM) is proposed in order to resolve overlapping peaks in liquid chromatography by using a conventional fluorescence detector. The method uses as analytical signals the heights or the areas obtained at two previously selected emission wavelengths, and good results are obtained for highly overlapping peaks with highly overlapping fluorescence spectra. The principal benefits of the method are the ease of finding the required wavelengths, its insensitivity to changes in the retention time of the peak from one injection to another, and the possibility of using it in highly or only partially overlapping peaks. We have applied the method to the determination of phenol and cresols in water, resolving by the proposed method the overlapping peaks ofm- andp-cresol.     

基于分形理论分辨重叠峰的新算法

将分形理论用于仪器分析信号的解析,提出一种面向分析谱图中重叠信号处理的分形分辨算法.通过对信号进行分形分析,采用分形维数可有效地反映信号的特征,准确地得到谱峰个数和位置的信息,避免人为判断的误差,实现重叠复合信号的分辨.实验表明,这种新的重叠谱峰分辨法能用于光谱、电化学、色谱等仪器分析数据的处理     

Dedicated mother wavelet in the determination of antimony in the presence of copper

In this paper, a new signal-processing procedure is applied to the optimization of voltammetric determination of antimony in the presence of copper and the parallel determination of these two elements. The proposed numerical algorithm for the separation of the overlapping peaks utilizes the continuous wavelet transform and the inverse continuous wavelet transform. As the base function, the specially defined dedicated mother wavelet is used. In its construction the ideal, simulated voltammetric peak is intensively exploited. This approach, corresponding to the wavelet theory, gives satisfactory signals separation, even in the cases when they constitute one peak. The possibility of Sb(III) determination is presented in the case of different distances between copper and antimony peaks and also in 10-, 20- and 50-fold excesses of Cu. The parallel determination of Cu(II) and Sb(III) is possible even in the case of a 10-fold excess of copper. The quality of the obtained results fulfills the requirements of validation.     

Parametric signal fitting by gaussian peak adjustment: A new multivariate curve resolution method for non-bilinear voltammetric measurements

A new methodology based on the fitting of signals to parametric functions is proposed for the multivariate curve resolution (MCR) analysis of overlapping and peak-shaped voltammetric signals which progressively get broader or narrower and move along the potential axis, thus causing a dramatic loss of linearity. The method is based on the least squares fitting of gaussian functions at both sides of the peaks by using adjustable parameters for the peak height, position and symmetry. It consists of several home-made programs written in Matlab environment, which are freely available as supplementary material of the present work. The application to the systems Zn(II)–oxalate, and to the phytochelatin PC₅ in a wide pH range provides excellent results as compared to these of more conventional linear methods, which raises good expectations about future application to electrochemical and even non-electrochemical data.     

Differential pulse voltammetric oxidation of polyriboxanthylic acid at the pyrolytic graphite electrode and a method for detection and determination of traces of xanthine and xanthosine-5'- monophosphate in polyxanthylic acid

Poly(X) (polyriboxanthylic acid) gives up to two differential pulse voltammetric oxidation peaks (peaks I and II) at the PGE. Xanthine, which appears to be a trace contaminant of commercial poly(X) samples, exhibits a differential pulse voltammetric oxidation peak at more negative potentials than the peaks of poly(X). Xanthosine-5'-monophosphate also gives up to two differential pulse voltammetric oxidation peaks at the PGE. An analytical method has been developed to determine trace amounts of xanthine and xanthosine-5'-monophosphate in poly(X) samples based on differential pulse voltammetry.     

Quantification of components in overlapping peaks from capillary electrophoresis by using continues wavelet transform method

The application of continues wavelet transform (CWT) for resolving overlapping peaks from capillary electrophoresis (CE) is described. Overlapping peaks can be resolved easily by transforming experimental signals into their wavelet coefficients. The proposed method was applied for the determination of benzoic acid and salicylic acid in overlapping peaks from CE. The composition of the two acids in Zuguangsan, a traditional Chinese patent medicine, was determined. The quantification results are satisfactory. CWT has been shown to be a practicable approach for resolving overlapping peaks and for quantitative determining coeluted compounds in overlapping peaks from CE. The quantification results obtained from CWT were compared with those obtained from numerical differentiation method. CWT has been shown prior to numerical differentiation method for processing experimental signals which contain noise.     

Determination of palladium by stripping voltammetry in raw gold ores

The electroconcentration of gold(III) and palladium(II) on the electrode surface gives a binary alloy whose components are electrochemically oxidized at almost the same potential. Two methods were proposed for the separation of overlapping anodic peaks: the chemical reduction of gold(III) under UV irradiation and the use of a special computer software built into the analyzer. The results of determining palladium(II) in raw gold ore using stripping voltammetry and two proposed methods of peak separation are compared.     

Chromatogram simulation by area reproduction

A modified Poisson function has been developed for the simulation of chromatographic peaks. The proposed model is shown to have the property of exactly recreating the experimentally determined peak area. Model parameters are obtained directly from the experimental peak, and overlapping peaks are deconvoluted such that the area sum of overlapping peaks is kept unchanged. The method was applied to real, complex chromatograms.     

基于无基底扣除的数据趋势累积谱峰检测算法

谱峰的检测分析在色谱技术研究中具有十分重要的作用,但在色谱数据采集、传输的过程中,不同程度的噪声干扰给谱峰检测带来了极大的困难.目前传统的谱峰检测算法普遍通过基底扣除的方式对谱峰的形态进行预定义,将谱峰分为单峰、重叠峰等多个种类.针对不同种类的谱峰采用不同的检测方法,这就导致了传统的谱峰检测算法具有高复杂度、低自动化程...     

A simple method to extract spectral parameters using fractional derivative spectrometry

The nonlinear fitting method, based on the ordinary least squares approach, is one of several methods that have been applied to fit experimental data into well-known profiles and to estimate their spectral parameters. Besides linearization measurement errors, the main drawback of this approach is the high variance of the spectral parameters to be estimated. This is due to the overlapping of individual components, which leads to ambiguous fitting. In this paper, we propose a simple mathematical tool in terms of a fractional derivative (FD) to determine the overlapping band spectral parameters. This is possible because of several positive effects of FD connected with the behavior of its zero-crossing and maximal amplitude. For acquiring a stable and unbiased FD estimate, we utilize the statistical regularization method and the regularized iterative algorithm when a priori constraints on a sought derivative are available. Along with the well-known distributions such as Lorentzian, Gaussian and their linear combinations, the Tsallis distribution is used as a model to correctly assign overlapping bands. To demonstrate the power of the method, we estimate unresolved band spectral parameters of synthetic and experimental infra-red spectra.     

Use of a data treatment software for the resolution of overlapping differential pulse polarographic peaks

Summary A procedure based on the use of the Beckman Data Leader Software is proposed for resolving binary mixtures of electroactive analytes when their differential pulse polarographic peaks are overlapping without any separation step. The resolution is made by measuring in the selected zero-crossings of the first derivative differential pulse polarograms. For testing the procedure, two well-known systems were used, cadmium (II)-indium (III) and thallium (I)-lead (II) mixtures. The four metallic ions can be determined in diverse ratios with quantification limits lower than 10^–7 mol/l.     

Analysis of enantiomers giving partially overlapped peaks by using different treatments of the chromatographic ultraviolet signals: quantification of pseudoephedrine enantiomers

Different strategies for the quantification of partially coeluting optical isomers have been investigated. The methods tested are based on the use of different features as the analytical UV signals: peak heights, perpendicular drop areas, first and second derivatives of the chromatograms, peak areas obtained by deconvolution of the overlapped peaks with data fitting optimization, and a multivariate model (principal component regression, PCR). The amphetamine-derivative drug pseudoephedrine was selected as a model compound. For chromatography, LiChrospher 100 RP₁₈ and a mobile-phase consisting of methanol and a solution of carboxymethyl-β-cyclodextrin (the chiral selector) were used. The UV detector was set at 215 nm. The accuracy obtained with the tested methods at different degrees of overlapping and at different concentration ratios between enantiomers was evaluated. The results of this study demonstrated that the best option for quantification of partially overlapped UV peaks of enantiomers and to obtain the enatiomeric excess is the use of a PCR model using peak heights, perpendicular drop peak areas and deconvoluted peak areas as the original variables. The predictive ability of the proposed calibration model is of about 2–8 times better (depending on the overlapping degree) than that achieved with the other models tested.     

Simultaneous Determination of Cadmium,Lead, Copper,and Thallium in Highly Saline Samples by Anodic Stripping Voltammetry (ASV) Using Mercury‐Film and Bismuth‐Film Electrodes

This paper describes a comparative study of the simultaneous determination of Cd(II), Pb(II), Tl(I), and Cu(II) in highly saline samples (seawater, hydrothermal fluids, and dialysis concentrates) by ASV using the mercury‐film electrode (MFE) and the bismuth‐film electrode (BiFE) as working electrodes. The features of MFE and BiFE as working electrodes for the single‐run ASV determinations are shown and their performances are compared with that of HMDE under similar conditions. It was observed that the stripping peak of Tl(I) was well separated from Cd(II) and Pb(II) peaks in all the studied saline samples when MFE was used. Because of the severe overlapping of Bi(III) and Cu(II) stripping peaks in the ASV using BiFE, as well as the overlapping of Pb(II) and Tl(I) stripping peaks in the ASV using HMDE, the simultaneous determination of these metals was not possible in highly saline medium using these both working electrodes. The detection limits calculated for the metals using MFE and BiFE (deposition time of 60 s) were between 0.043 and 0.070 μg L^?1 for Cd(II), between 0.060 and 0.10 μg L^?1 for Pb(II) and between 0.70 and 8.12 μg L^?1 for Tl(I) in the saline samples studied. The detection limits calculated for Cu(II) using the MFE were 0.15 and 0.50 μg L^?1 in seawater/hydrothermal fluid and dialysis concentrate samples, respectively. The methods were applied to the simultaneous determination of Cd(II), Pb(II), Tl(I), and Cu(II) in samples of seawater, hydrothermal fluids and dialysis concentrates.     

Semi-Quantitative MALDI Measurements of Blood-Based Samples for Molecular Diagnostics

Accurate and precise measurement of the relative protein content of blood-based samples using mass spectrometry is challenging due to the large number of circulating proteins and the dynamic range of their abundances. Traditional spectral processing methods often struggle with accurately detecting overlapping peaks that are observed in these samples. In this work, we develop a novel spectral processing algorithm that effectively detects over 1650 peaks with over 3.5 orders of magnitude in intensity in the 3 to 30 kD m/z range. The algorithm utilizes a convolution of the peak shape to enhance peak detection, and accurate peak fitting to provide highly reproducible relative abundance estimates for both isolated peaks and overlapping peaks. We demonstrate a substantial increase in the reproducibility of the measurements of relative protein abundance when comparing this processing method to a traditional processing method for sample sets run on multiple matrix-assisted laser desorption/ionization-time of flight (MALDI-TOF) instruments. By utilizing protein set enrichment analysis, we find a sizable increase in the number of features associated with biological processes compared to previously reported results. The new processing method could be very beneficial when developing high-performance molecular diagnostic tests in disease indications.