A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods--the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method--were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3.3H2O and PrCl3.6H2O were obtained using the proposed CWT method; the results are satisfactory.     

Approximate derivative calculated by using continuous wavelet transform

A novel method of calculating approximate derivative of signals in analytical chemistry by using the continuous wavelet transform (CWT) is proposed. As compared with numerical differentiation, FT method and DWT method, fast calculation, and simple mathematical operation are remarkable advantages of CWT method. The signal-to-noise ratio (SNR) of approximate derivative of signals calculated by CWT method is easily enhanced only through appropriately adjusting the dilation, even in the case of very low SNR. Therefore, CWT method is a powerful tool for performing the approximate derivative calculation of signals in analytical chemistry. Additionally, the approximate second derivative evaluated via CWT method can be used to determine the peak potentials of the overlapping square wave voltammogram (SWV) of Cd(II) and In(III), and the results are very satisfactory.     

A continuous wavelet transform algorithm for peak detection

Contactless conductivity detector technology has unique advantages for microfluidic applications. However, the low S/N and varying baseline makes the signal analysis difficult. In this paper, a continuous wavelet transform-based peak detection algorithm was developed for CE signals from microfluidic chips. The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm by Du et al. [Bioinformatics 2006, 22, 2059-2065], and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function. It forms sequences of local maxima and minima in the continuous wavelet transform, before pairing sequences of maxima to minima to define peaks. The peak detection algorithm was tested against the Cromwell, MassSpecWavelet, and Linear Matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometer Peak Indication and Classification algorithms using experimental data. Its sensitivity to false discovery rate curve is superior to other techniques tested.     

Feature analysis of protein structure by using discrete Fourier transform and continuous wavelet transform

In this paper, discrete Fourier transform (DFT) and continuous wavelet transform (CWT) are used to predict the protein structure. Hydrophobicity plays a key role in the form of protein structure. The amino acid sequence is first mapped into hydrophobicity sequence, and then process it by DFT and CWT so that power spectral density is gained. The results show that continuous wavelet transform can extract the features of protein structure effectively and availably and has a tremendous development foreground.     

Multicomponent quantitative resolution of binary mixtures by using continuous wavelet transform

Continuous 1-dimensional wavelet transform (WT) was applied to the quantitative analysis of a vitamin combination of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) with strongly overlapping signals. Absorbance data from the UV-Vis absorption spectrum of width 1150 were subjected to Gauss1 and Gauss2 WTs. Because of its flexibility, data processing, and its high signal amplitude, the continuous WT method is a powerful tool for analysis of multicomponent mixtures. By measuring the amplitude signals corresponding to the selected zero-crossing points of the transformed signal, we obtained the calibration curve. The validation of the calibration graphs was confirmed with different mixtures of THI and PYR at various concentration ratios. A brief explanation of the continuous wavelet method is given. MATLAB 6.5 software was used to perform the calculations. The results of our study were compared with those obtained by spectroscopic, chemometric, and liquid chromatographic methods, and good agreement was found.     

Maximum spectrum of continuous wavelet transform and its application in resolving an overlapped signal

To estimate the number of peaks and to find the individual peak positions in an overlapped signal, a new method called maximum spectrum of continuous wavelet transform (MSCWT) was developed by extracting the maximum coefficients of continuous wavelet transform (CWT). The peak position in MSCWT was the same as that in its original signal. In this process, CWT was performed not on a single dilation but on an appreciation dilation range. To obtain such a range, a new criterion was introduced to choose a center dilation, which was used to form the dilation range. If Cdilation denoted the center dilation, the proper dilation range was [Cdilation -6 +/- 2, Cdilation +1 +/- 1]. The Mexican Hat function was an analytical wavelet. Utilizing the information of the peak number and the position detected by MSCWT, a fitting route was performed to recover the original signal. One simulated and four true overlapped signals, including high performance liquid chromatography (HPLC), ultraviolet-visible (UV) spectrum, and differential pulse voltammetric (DPV), were processed, and the results indicated that MSCWT could detect an overlapped peak number and position, and the curve fitting based on information of MSCWT had a higher accuracy. The proposed method was an efficient one in resolving different types of overlapped signals.     

About using the approximate fields to calculate the electrostatic potential distribution of membrane channels

By the example of gramicidine channel, a comparative analysis of different approximate representations (heavy atoms, polar protons, near-by atoms) of AMBER force field has been carried out to calculate the electrostatic potential distribution of ionic channels in biological membranes. The results obtained are compared with the potential computed in a full-atom representation. The use of approximate representations is shown to lead to estimated errors of the potential.     

Prediction of transmembrane proteins based on the continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) for predicting the number and location of helices in membrane proteins is presented. Two bacteria proteins are chosen as examples to describe the prediction of transmembrane helices (HTM) by using this method. Selections of an appropriate dilation and hydrophobicity data types are discussed in the text. The results indicate that CWT is a promising approach for the prediction of HTM.     

Determination of bismuth and copper using adsorptive stripping voltammetry couple with continuous wavelet transform

A new method is proposed for the determination of bismuth and copper in the presence of each other based on adsorptive stripping voltammetry of complexes of Bi(III)-chromazorul-S and Cu(II)-chromazorul-S at a hanging mercury drop electrode (HMDE). Copper is an interfering element for the determination of Bi(III) because, the voltammograms of Bi(III) and Cu(II) overlapped with each other. Continuous wavelet transform (CWT) was applied to separate the voltammograms. In this regards, wavelet filter, resolution of the peaks and the fitness were optimized to obtain minimum detection limit for the elements. Through continuous wavelet transform Symlet4 (Sym4) wavelet filter at dilation 6, quantitative and qualitative analysis the mixture solutions of bismuth and copper was performed. It was also realized that copper imposes a matrix effect on the determination of Bi(III) and the standard addition method was able to cope with this effect. Bismuth does not have matrix effect on copper determination, therefore, the calibration curve using wavelet coefficients of CWT was used for determination of Cu(II) in the presence of Bi(III). The detection limits were 0.10 and 0.05 ng ml⁻¹ for bismuth and copper, respectively. The linear dynamic range of 0.1-30.0 and 0.1-32.0 ng ml⁻¹ were obtained for determination of bismuth in the presence of 24.0 ng ml⁻¹ of copper and copper in the presence of 24.0 ng ml⁻¹ of bismuth, respectively. The method was used for determination of these two cations in water and human hair samples. The results indicate the ability of method for the determination of these two elements in real samples.     

Determination of chlorogenic acid in plant samples by using near-infrared spectrum with wavelet transform preprocessing.

By theoretical analysis, it is found that wavelet transform (WT) with a wavelet function can be regarded as a smoothing and a differentiation process, and that the order of differentiation is determined by the vanishing moment, which is an important property of a wavelet function. Therefore, a method based on the continuous wavelet transform (CWT) for removing the background in the near-infrared (NIR) spectrum is proposed, and it is used in the determination of the chlorogenic acid in plant samples as a preprocessing tool for partial least square (PLS) modeling. It is shown that the benefit of the proposed method lies not only in its performance to improve the quality of PLS model and the prediction precision, but also in its simplicity and practicability. It may become a convenient and efficient tool for preprocessing NIR spectral data sets in multivariate calibration.     

Detecting the quality of glycerol monolaurate: A method for using Fourier transform infrared spectroscopy with wavelet transform and modified uninformative variable elimination

Glycerol monolaurate (GML) products contain many impurities, such as lauric acid and glucerol. The GML content is an important quality indicator for GML production. A hybrid variable selection algorithm, which is a combination of wavelet transform (WT) technology and modified uninformative variable eliminate (MUVE) method, was proposed to extract useful information from Fourier transform infrared (FT-IR) transmission spectroscopy for the determination of GML content. FT-IR spectra data were compressed by WT first; the irrelevant variables in the compressed wavelet coefficients were eliminated by MUVE. In the MUVE process, simulated annealing (SA) algorithm was employed to search the optimal cutoff threshold. After the WT-MUVE process, variables for the calibration model were reduced from 7366 to 163. Finally, the retained variables were employed as inputs of partial least squares (PLS) model to build the calibration model. For the prediction set, the correlation coefficient (r) of 0.9910 and root mean square error of prediction (RMSEP) of 4.8617 were obtained. The prediction result was better than the PLS model with full-spectra data. It was indicated that proposed WT-MUVE method could not only make the prediction more accurate, but also make the calibration model more parsimonious. Furthermore, the reconstructed spectra represented the projection of the selected wavelet coefficients into the original domain, affording the chemical interpretation of the predicted results. It is concluded that the FT-IR transmission spectroscopy technique with the proposed method is promising for the fast detection of GML content.     

A variational method to calculate static electronic properties

Using a coupled cluster form of the wave function, a variational method is formulated for calculation of static properties of any order. Corresponding to an appropriate perturbed hamiltonian H() including the relevant static property, a size consistent functional is set up. In a hierarchical fashion, properties of different orders may be found out using a variational method.     

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.     

An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Summary Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.     

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.     

An approximate density-functional method using the Harris-Foulkes functional

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the errors of reference-geometry Harris-Foulkes (compared to full self-consistent Kohn-Sham) for the PBE exchange-correlation functional have the same magnitude as the difference between the energies of PBE and BLYP.     

Signals ratio method combined with wavelet transform: application to resolution of overlapped electrochemical signals

A signals ratio method combined with wavelet transform was proposed for the resolution of a weak voltammetric signal overlapped by other components. The signals ratio method usually suffers from interference from noise and baseline contained in the original signals because these factors cause distortion of the signals ratio. The multiresolution capability of the wavelet transform method was exploited here to simultaneously remove or reduce the noise and background. As a result, a deformation-free signals ratio with good signal-to-noise ratio (SNR) was obtained even for very noisy signals. The properties of the proposed method were compared to other resolution methods. It was demonstrated that the combined signals ratio wavelet transform method was particularly applicable to resolve a minor component in the presence of large amount of other components, suggesting that it can provide improved detection limits and quantified results for minor components. The method was employed for the voltammetric determination of residual chlorine in the presence of N,N-diethyl-p-phenylenediamine (DPD).     

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.     

A new grand canonical ensemble method to calculate first-order phase transitions

A theory about first-order phase transition of pure fluids is proposed. The theory is developed by combining grand canonical ensemble with density functional for homogeneous fluids. It is based on the fact that the grand partition function of one macroscopic volume is the product of the grand partition functions of its subvolumes. Density fluctuations of molecules determine the relation between the grand partition function and the free energy density. By combining pairs of subvolumes successively, the free energy density is transformed and rapidly becomes stationary. The stationary curve versus molecule density is convex and its linear segments represent phase transitions. The transform leads to the new grand canonical method to calculate phase equilibrium, which is more robust than classic ones. The transform suggests that classical van der Waals loop is physical and essential to phase transition.