Zhongxiao Pan

Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis

Abstract Wavelet transform has been proven to be a high performance signal processing technique. In this paper, a novel algorithm which is more suitable to process analytical signals is proposed, and application of the algorithm in denoising, baseline correction, determination of component number in overlapping chromatograms, and preprocessing the data matrix for window factor analysis (WFA) in resolving multi-component overlapping chromatograms is reported. The main characteristic of the wavelet transform is that it decomposes a signal into localized contributions, and each of the contributions represents the information of different frequency contained in the original signal. Therefore, the noise can be filtered by separating the high frequency contributions from the chromatogram, the baseline correction can be obtained by removing the low frequency contributions from the chromatogram, and the resolved chromatogram can be retrieved from the overlapping signal by choosing a discrete detail at certain scales from the decomposed contributions. The determination of component number in overlapping chromatograms can be obtained by simply counting the number of peaks in the resolved chromatogram.

Optimization of Lennard-Jones atomic clusters

A fast annealing evolutionary algorithm was applied to determine the minimum configurations of Lennard-Jones (LJ) clusters. Other techniques such as limited memory quasi-Newton algorithm (L-BFGS), seeding, similarity checking, and moving, were also used in this method. It has been shown that these techniques dramatically speed up the evolutionary procedure. The lowest known energies were located for the LJ clusters containing up to 74 atoms. It has been proven that the algorithm is a fast and high efficient optimizing tool, which can be used in energy minimization problems.

A new stochastic resonance algorithm to improve the detection limits for trace analysis

Based on the stochastic resonance theory, a new stochastic resonance algorithm (SRA) to improve analytical detection limits for trace analysis is presented. In the new algorithm, stochastic resonance takes place in a bistable system driven only by the inherent noise of an analytical signal. The effect of the system parameters on the proposed algorithm is discussed and the optimization of parameters is studied. By using experimental chromatographic and spectroscopic data sets, it is proven that the signal-to-noise ratio (SNR) of the analytical signal can be greatly enhanced by the method, and an excellent quantitative relationship between different concentrations and their responses can be obtained. Stochastic resonance may be a promising tool to extend instrumental linear range and to improve the accuracy of micro- or trace analysis.

A method based on stochastic resonance for the detection of weak analytical signal.

An effective method for detection of weak analytical signals with strong noise background is proposed based on the theory of stochastic resonance (SR). Compared with the conventional SR-based algorithms, the proposed algorithm is simplified by changing only one parameter to realize the weak signal detection. Simulation studies revealed that the method performs well in detection of analytical signals in very high level of noise background and is suitable for detecting signals with the different noise level by changing the parameter. Applications of the method to experimental weak signals of X-ray diffraction and Raman spectrum are also investigated. It is found that reliable results can be obtained.

Global optimization of (C60)N molecular clusters

Abstract A parallel fast annealing evolutionary algorithm (PFAEA) was employed to optimize the structures of (C 60 ) N molecular clusters with the lowest energy based on an intermolecular potential developed by Girifalco. Although it is very difficult to locate their lowest energy minima for the short range of the potential of C 60 molecular clusters, the known lowest energy structures up to N =80, including icosahedral, decahedral, close-packed, have been found successfully by using this effective optimizing tool. Furthermore, two new global energy minima of (C 60 ) 30 and (C 60 ) 62 were also located in this work.

Chiral recognition study for the inclusion complexes of amino acids with α-cyclodextrin using a fast annealing evolutionary algorithm

Abstract Molecular interactions of inclusion complexes of amino acids and α-cyclodextrin have been studied by a fast annealing evolutionary algorithm (FAEA) in this paper. Using the consistent force field (CFF91), the non-bonded energies between all pairs of atoms in different molecules were determined by a Coulomb potential term for electrostatic interactions and a Lennard–Jones potential for van der Waals interactions. The total interaction energies for 14 inclusion complexes with experimental association constants (ln K) were optimized by the FAEA method. Linear regression analysis of the observed association constants against the total energies was performed. The result indicated that there is an extremely good correlation between ln K and the total interaction energies. Furthermore, by analyzing each energy term, the van der Waals term is the major contributor to the total energies and the electrostatic force is also important in inclusion complexation. In the 14 inclusion complexes, four pairs of l -/ d -amino acids were compared. The interaction energies of α-cyclodextrin with the l -amino acids are lower than the energies with the d -enantiomers. It is in agreement with the experimental results. The enantioselectivity can, therefore, be calculated from the complexation energies of l -/ d -amino acids.

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.

Molecular docking of α-cyclodextrin inclusion complexes by genetic algorithm and empirical binding free energy function

Abstract A molecular docking method that predicts the lowest energy geometries of inclusion complexes between host and guests was developed and tested, in combination with a new simple empirical function that estimates the free energy of binding. The total interaction energies of the host–guest inclusion complexes were optimized using a genetic algorithm (GA). The docking method was applied to 43 complexes of α-cyclodextrin (α-CD) and mono- or 1,4-disubstituted benzenes with known binding constants. The new simple empirical free energy function was calibrated by the 43 docked complex structures and gave a good relationship between the predicted binding constants and the observed values.

A Wavelet-Based Genetic Algorithm for Compression and De-Noising of Chromatograms

ABSTRACT A wavelet-based genetic algorithm using real-number coding and arithmetical crossover method in signal processing is described in this work. Due to the characteristic of the wavelet, an analytical signal can be represented by a finite linear combination of wavelet-based functions. Using a wavelet-based genetic algorithm to find the coefficients to such representation, an analytical signal can be reconstructed by the coefficients and the corresponding elementary function. Therefore the method can be used to compress and de-noise analytical signals because the insignificant information such as noise will not be reserved in the reconstructed signal. Both simulated signals and experimental multicomponent chromatograms are successfully compressed and de-noised with the proposed algorithm.