Fractional wavelet analysis for the simultaneous quantitative analysis of lacidipine and its photodegradation product by continuous wavelet transform and multilinear regression calibration

Fractional wavelet transform (FWT) was applied to the original absorption spectra of lacidipine (LAC) and its photodegradation product (LACD), and the resulting FWT spectra were processed by continuous wavelet transform (CWT) and multilinear regression calibration (MLRC) for the simultaneous quantitative analysis of both products in their binary mixtures. These methods do not require any chemical separation step and chemical complex reaction to obtain a detectable signal for the degradation product. By using the Mexican hat function, 2 calibration functions for LAC and LACD were obtained by measuring the CWT transformed signals at 416.1 nm for LAC and 414.6 nm for LACD, after FWT processing of the original absorption spectra. The calibration graphs were linear in the concentration range of 5.08-40.64 microg/mL for LAC and 0.51-8.16 microg/mL for LACD. The limit of detection and the limit of quantitation were found to be 0.289 and 0.956 microg/mL for LAC and 0.036 and 0.118 microg/mL for LACD, respectively. For comparison, the MLRC algorithm was applied to the linear regression functions for the individual drug and its photoproduct. In this approach, a set of linear regression functions was obtained from the relationship between concentrations and FWT signals in the wavelength range 411.0-412.4 nm. Both methods were applied to the quantitative evaluation of LAC and LACD in laboratory and pharmaceutical samples, and produced very satisfactory results.     

离散小波变换-支持向量回归方法同时测定苯酚、苯胺和苯甲酸

在波长范围200～400nm测定苯酚、苯胺和苯甲酸混合液的吸收光谱,用离散小波变换（DWT）对光谱数据进行处理,再用支持向量回归SVR方法进行建模,建立了离散小波变换一支持向量回归方法（DWT—SVR）。方法用于模拟样品和污染水样中苯酚、苯胺和苯甲酸的同时测定,结果满意。     

Elimination of interference information by a new hybrid algorithm for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the interference information for multivariate calibration of near-infrared (NIR) spectra that includes noise, background and systemic spectral variation irrelevant to concentration. The method consists of two parts: approximate derivative based on continuous wavelet transform (CWT) and orthogonal signal correction (OSC). After the approximate derivative calculated by CWT, OSC was performed. It was successfully applied to real complex NIR spectral data to eliminate the interference information. Correction for the interference of NIR spectra resulted in a substantial improvement in the predicted precision, and a more concise calibration model was obtained. The proposed procedure also compared favourably with several pretreatment methods, and the new method appears to provide a high-performance pretreatment tool for multivariate calibration of NIR spectra. In addition, the strategy proposed here can be applied to various other spectral data for quantitative purposes as well.     

Interpolation by fast Wigner transform for rapid calculations of magnetic resonance spectra from powders

We introduce a novel interpolation strategy, based on nonequispaced fast transforms involving spherical harmonics or Wigner functions, for efficient calculations of powder spectra in (nuclear) magnetic resonance spectroscopy. The fast Wigner transform (FWT) interpolation operates by minimizing the time-consuming calculation stages, by sampling over a small number of Gaussian spherical quadrature (GSQ) orientations that are exploited to determine the spectral frequencies and amplitudes from a 10-70 times larger GSQ set. This results in almost the same orientational averaging accuracy as if the expanded grid was utilized explicitly in an order of magnitude slower computation. FWT interpolation is applicable to spectral simulations involving any time-independent or time-dependent and noncommuting spin Hamiltonian. We further show that the merging of FWT interpolation with the well-established ASG procedure of Alderman, Solum and Grant [J. Chem. Phys. 134, 3717 (1986)] speeds up simulations by 2-7 times relative to using ASG alone (besides greatly extending its scope of application), and between 1-2 orders of magnitude compared to direct orientational averaging in the absence of interpolation. Demonstrations of efficient spectral simulations are given for several magic-angle spinning scenarios in NMR, encompassing half-integer quadrupolar spins and homonuclear dipolar-coupled (13)C systems.     

Multielement atomic absorption analysis using Hadamard transform spectroscopy with a new computation and superposition procedure

The application of Hadamard transform spectroscopy (HTS) to analytical atomic spectroscopy has been investigated. A theoretical examination of the signal to noise ratio indicates that HTS offers a slight multiplex advantage over single slit scanning of the spectrum for the measurement of intense lines, as in atomic absorption, but is disadvantageous for measuring small signals in atomic emission and fluorescence. Using a simple HT spectrometer Mg and Pb were determined simultaneously by flame atomic absorption spectrometry. Sensitivities similar to those of conventional systems were obtained but, owing to instrumental imperfections and a short data collection time, detection limits were worse. Optimum system performance was obtained when the mask interval width was equal to the width of the image of the spectrometer entrance slit. Greater spectral detail was revealed by superposition of a set of computed spectra in which the starting point of each spectrum was displaced from the others by a distance less than the interval width of the Hadamard mask. This approach gave improved spectra without increased instrumental complexity.     

Combining orthogonal signal correction and wavelet packet transform with partial least squares to analyze overlapping spectra of three kinds of metal ions

A novel method named OSC-WPT-PLS approach based on partial least squares (PLS) regression with orthogonal signal correction (OSC) and wavelet packet transform (WPT) as pre-processed tools was proposed for the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). This method combines the ideas of OSC and WPT with PLS regression for enhancing the ability of extracting characteristic information and the quality of regression. OSC is used to remove information in the response matrix D by subtracting the structured noise that is orthogonal to the concentration matrix C. Wavelet packet transform was applied to perform data compression, to extract relevant information, and to eliminate noise and collinearity. PLS was applied for multivariate calibration and noise reduction by eliminating the less important latent variables. In this case, using trials, the kind of wavelet function, the decomposition level, the number of OSC components and the number of PLS factors for the OSC-WPT-PLS method were selected as Daubechies 4, 3, 2 and 3, respectively. A program (POSCWPTPLS) was designed to perform the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). The relative standard errors of prediction (RSEP) obtained for total elements using OSC-WPT-PLS, WPT-PLS and PLS were compared. Experimental results demonstrated that the OSC-WPT-PLS method had the best performance among the three methods and was successful even when there was severe overlap of spectra.     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis

A new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml⁻¹ for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. Matlab 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.     

On the calculation of circular dichroism spectra using quantum wave-packet dynamics with an application to molecular dimers

Circular dichroism (CD) spectra are calculated from the Fourier transform of a time-correlation function. The latter can efficiently be evaluated by wave-packet propagation methods. This approach is similar to the time-dependent evaluation of absorption or Raman spectra. As an application, correlation functions and CD spectra for a molecular dimer are determined and compared to the case of absorption.     

Determination of sodium benzoate by chiral ligand exchange CE based on its inhibitory activity in D-amino acid oxidase mediated oxidation of D-serine

A novel quantitative approach for the determination of sodium benzoate (SB) was proposed by the kinetic study about its competitive inhibitory efficiency to D-amino acid oxidase (DAAO) activity with a chiral ligand exchange capillary electrophoresis (CE) method, in which the Zn(II)-L-prolinamide complex was chosen as a novel chiral selector. After the optimization of buffer pH and the chiral selector concentration this chiral ligand exchange CE method was employed to determine labeled D,L-Serine with good linearity (r(2)≥0.995), efficient recovery (95.6-100.9%) and remarkable reproducibility (RSD≤1.2%). This chiral separation method was further used to observe DAAO activity through the determination of D-Serine concentration variation after being incubated with DAAO and obtain the sigmoidal inhibitory curve of SB to DAAO activity. The ascending part of this inhibitory curve was linearly fitted in a limited range for SB from 2.0 to 200 μM with an appropriate coefficient of determination (R(2)=0.990). The linearity was then validated to be a promising method for the analysis of SB with the standout merits of high selectivity and adjustable detection range. Furthermore, this proposed method was used for the pharmacokinetics study of SB.     

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 new hybrid strategy for constructing a robust calibration model for near-infrared spectral analysis

A new hybrid algorithm is proposed for construction of a high-quality calibration model for near-infrared (NIR) spectra that is robust against both spectral interference (including background and noise) and multiple outliers. The algorithm is a combination of continuous wavelet transform (CWT) and a modified iterative reweighted PLS (mIRPLS) procedure. In the proposed algorithm the spectral interference is filtered by CWT at the first stage then mIRPLS is proposed to detect the multiple outliers in the CWT domain. Compared with the original IRPLS method, mIRPLS does not need to adjust variable parameters to achieve optimum calibration results, which makes it very convenient to perform in practice. The final PLS model is constructed robustly because both the spectral interference and multiple outliers are eliminated. In order to validate the effectiveness and universality of the algorithm, it was applied to two different sets of NIR spectra. The results indicate that the proposed strategy can greatly enhance the robustness and predictive ability of NIR spectral analysis.     

New cut-off criterion for uninformative variable elimination in multivariate calibration of near-infrared spectra for the determination of heroin in illicit street drugs

A new cut-off criterion has been proposed for the selection of uninformative variables prior to chemometric partial least squares (PLS) modelling. After variable elimination, PLS regressions were made and assessed comparing the results with those obtained by PLS models based on the full spectral range. To assess the prediction capabilities, uninformative variable elimination (UVE)-PLS and PLS were applied to diffuse reflectance near-infrared spectra of heroin samples. The application of the proposed new cut-off criterion, based on the t-Students distribution, provided similar predictive capabilities of the PLS models than those obtained using the original criteria based on quantile value. However, the repeatability of the number of selected variables was improved significantly.     

Enzymatic‐catalyzed polymerization of water‐soluble electrically conductive polymer PEDOT:PSS

Water‐soluble electrically conductive polymer poly(3,4‐ethylenedioxythiophene) (PEDOT) was synthesized by the enzymatic‐catalyzed method using 3,4‐ethylenedioxythiophene (EDOT) as monomer, poly(styrenesulfonate) (PSS) as water‐soluble polyelectrolyte, horseradish peroxidase enzyme as catalyst, and hydrogen peroxide (H₂O₂) as oxidant. Fourier transform infrared spectra and UV–vis absorption spectra confirm the successful enzymatic‐catalyzed polymerization of PEDOT. Dynamic light scattering data confirm the formation of a stable PEDOT:PSS aqueous dispersion. The thermo gravimetric data show that the obtained PEDOT is stable over a fairly high range of temperatures. The atomic force microscopy height images show that the PEDOT:PSS aqueous dispersion can form excellent homogeneous and smooth films on various substrates by conventional solution processing techniques, which renders this PEDOT:PSS aqueous dispersion a very promising candidate for various application in electronic devices. This enzymatic polymerization is a new approach for the synthesis of optical and electrical active PEDOT polymer, which benefits simple setting, high yields, and environmental friendly route. Copyright © 2014 John Wiley & Sons, Ltd.     

Minimisation of instrumental noise in the acquisition of FT-NIR spectra of bread wheat using experimental design and signal processing techniques

Spectral resolution (R) and number of repeated scans (S) have a significant effect on the S/N ratio of Fourier transform-near infrared (FT-NIR) spectra, but the optimal values of these two parameters have to be determined empirically for a specific problem, considering separately both the nature of the analysed matrix and the specific instrumental setup. To achieve this aim, the instrumental noise of replicated FT-NIR spectra of wheat samples was modelled as a function of R and S by means of the Doehlert design. The noise amounts in correspondence to different experimental conditions were estimated by analysing the variance signals derived from replicate measurements with two different signal processing tools, Savitzky–Golay (SG) filtering and fast wavelet transform (FWT), in order to separate the “pure” instrumental noise from other variability sources, which are essentially connected to sample inhomogeneity. Results confirmed that R and S values leading to minimum instrumental noise can vary considerably depending on the type of analysed food matrix and on the different instrumental setups, and helped in the selection of the optimal measuring conditions for the subsequent acquisition of a wide spectral dataset.     

A high-resolution scanning microprobe matrix-assisted laser desorption/ionization ion source for imaging analysis on an ion trap/Fourier transform ion cyclotron resonance mass spectrometer

A new scanning microprobe matrix-assisted laser desorption/ionization (SMALDI) ion source for high spatial resolution has been developed for linear ion trap and Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS). The source is fully compatible with commercial ion trap flanges (such as the LTQ series, Thermo Fisher Scientific). The source is designed for atmospheric pressure (AP) operation but is also suitable for mid-pressure operation. The AP mode is especially useful for investigating volatile compounds. The source can be interchanged with other ion sources within a minute when operated in the AP mode. Combining high-lateral resolution MALDI imaging with high mass resolution and high mass accuracy mass spectrometry, available in the FT-ICR mode, provides a new quality of analytical information, e.g. from biological samples. First results obtained with the new ion source demonstrate a maximum lateral resolution of 0.6 by 0.5 microm. Depending on the limit of detection of the chosen mass analyzer, however, the size of the focus had to be enlarged to a diameter of up to 8 microm in the FT-ICR mode, in order to create enough ions for detection. Mass spectra acquired for analytical imaging were obtained from single laser pulses per pixel in all the experiments. This mode allows us to investigate biological thin sections with desorption focus diameters in the micrometer range, known to cause complete evaporation of material under the laser focus with a very limited number of laser pulses. As a first example, peptide samples deposited in microstructures were investigated with the new setup. A high quality and validity of the acquired images were obtained in the ion trap mode due to the low limit of detection. High mass resolution and accuracy but poorer image quality were obtained in the ICR mode due to the lower detection sensitivity of the ICR detector.     

Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer

The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing measurements can be handled in a reliable and simple manner by assigning large measurement uncertainties to them. The problem of missing data is pervasive in chemistry, and MLPCA is applied to three sets of experimental data to illustrate its utility. For exploratory data analysis, a data set from the analysis of archeological artifacts is used to show that the principal components extracted by MLPCA retain much of the original information even when a significant number of measurements are missing. Maximum likelihood projections of censored data can often preserve original clusters among the samples and can, through the propagation of error, indicate which samples are likely to be projected erroneously. To demonstrate its utility in modeling applications, MLPCA is also applied in the development of a model for chromatographic retention based on a data set which is only 80% complete. MLPCA can predict missing values and assign error estimates to these points. Finally, the problem of calibration transfer between instruments can be regarded as a missing data problem in which entire spectra are missing on the ‘slave’ instrument. Using NIR spectra obtained from two instruments, it is shown that spectra on the slave instrument can be predicted from a small subset of calibration transfer samples even if a different wavelength range is employed. Concentration prediction errors obtained by this approach were comparable to cross-validation errors obtained for the slave instrument when all spectra were available.     

Variable selection by modified IPW (iterative predictor weighting)-PLS (partial least squares) in continuous wavelet regression models

Variable selection is often used to produce more robust and parsimonious regression models. But when they are applied directly to the raw near-infrared spectra, it is not easy to select appropriate variables because background and noise will often overshadow or overlap the absorption bands of analyte. In this work, a new hybrid algorithm based on the selection of the most informative variables in the continuous wavelet transform (CWT) domain is described. The strategy is a combination of CWT and a procedure of modified iterative predictor weighting-partial least square (mIPW-PLS). After elimination of the background and noise in NIR spectra by CWT, the mIPW-PLS approach is used to select the most informative CWT coefficients. With the selected CWT coefficients, a PLS model is built finally for prediction. It is indicated that the extraction of most important variables in the CWT domain can effectively avoid the interference of background and noise, and result in a high quality of regression model with a very small number of variables and fewer PLS components.     

Fractional-continuous wavelet transforms and ultra-performance liquid chromatography for the multicomponent analysis of a ternary mixture containing thiamine, pyridoxine, and lidocaine in ampules

New chemometric approaches based on the application of partial least squares (PLS) and principal component regression (PCR) algorithms with fractional wavelet transform (FWT) and continuous wavelet transform (CWT) are proposed for the spectrophotometric multicomponent determination of thiamine hydrochloride (B1), pyridoxine hydrochloride (B6), and lidocaine hydrochloride (LID) in ampules without any separation step. In this study PLS and PCR techniques were applied to the raw spectral data, FWT-coefficients, and FWT-CWT-coefficients. These calibration models were labeled as Raw-PLS and Raw-PCR, FWT-PLS and FWT-PCR, and FWT-CWT-PLS and FWT-CWT-PCR, respectively. A new ultra-performance liquid chromatographic (UPLC) method was developed for the comparison of the results obtained by applying the chemometric calibration methods. Chromatographic separation and determination of B1, B6, and LID in ampules were performed on an Acquity UPLC BEH C18 column (50x2.1 mm id, 1.7 pm particle size) using gradient elution with a mobile phase consisting of methanol and 0.01 M HCI at a constant flow rate of 0.6 mL/min. These combined chemometric calibrations and UPLC were validated by analyzing various ternary mixtures, B1, B6, and LID. The proposed chemometric approaches (signal processing-multivariate calibrations) and UPLC method were applied to the quantitative multicomponent analysis of marketed ampules containing the vitamins B1 and B6 with LID.     

A method for near-infrared spectral calibration of complex plant samples with wavelet transform and elimination of uninformative variables

An algorithm is proposed for extracting relevant information from near-infrared (NIR) spectra for multivariate calibration of routine components in complex plant samples. The algorithm is a combination of wavelet transform (WT) data compression and a procedure for uninformative variable elimination (UVE). After compression of the NIR spectra by WT, the UVE approach is used to eliminate the irrelevant wavelet coefficients. Finally, a calibration model is built from the retained wavelet coefficients to enable prediction. Because irrelevant information can be removed from the spectra used for multivariate calibration, the model based on the extracted relevant features is better than those obtained with full-spectrum data. Both prediction precision and calculation speed are improved.