Analysis of amoxicillin in human urine by photo-activated generation of fluorescence excitation-emission matrices and artificial neural networks combined with residual bilinearization

Fluorescence excitation-emission data recorded for amoxicillin after photo-activated reaction with periodate have been processed by a novel second-order multivariate method based on the combination of artificial neural networks and residual bilinearization (ANN/RBL), since the signals bear a strong non-linear relation with the analyte concentration. The selected chemometric methodology is employed for the first time to evaluate experimental non-linear second-order spectral information. Due to severe overlapping between the emission profiles for the analyte reaction product and for the urine background, calibration was done using different spiked urine samples. This allowed for the determination of amoxicillin in test spiked urines, other than those employed for calibration. When new urine samples containing a fluorescent anti-inflammatory were analyzed, accurate prediction in the presence of unexpected components required the achievement of the second-order advantage, which is provided by the post-training RBL procedure. Amoxicillin was also determined by ANN/RBL in a series of real urine samples, which allowed one to perform a comparison study with the reference high-performance liquid chromatographic technique.     

Identification and quantification of carbamate pesticides in dried lime tree flowers by means of excitation-emission molecular fluorescence and parallel factor analysis when quenching effect exists

A non-separative, fast and inexpensive spectrofluorimetric method based on the second order calibration of excitation-emission fluorescence matrices (EEMs) was proposed for the determination of carbaryl, carbendazim and 1-naphthol in dried lime tree flowers. The trilinearity property of three-way data was used to handle the intrinsic fluorescence of lime flowers and the difference in the fluorescence intensity of each analyte. It also made possible to identify unequivocally each analyte. Trilinearity of the data tensor guarantees the uniqueness of the solution obtained through parallel factor analysis (PARAFAC), so the factors of the decomposition match up with the analytes. In addition, an experimental procedure was proposed to identify, with three-way data, the quenching effect produced by the fluorophores of the lime flowers. This procedure also enabled the selection of the adequate dilution of the lime flowers extract to minimize the quenching effect so the three analytes can be quantified. Finally, the analytes were determined using the standard addition method for a calibration whose standards were chosen with a D-optimal design.     

A Volterra Series Approach to the Approximation of Stochastic Nonlinear Dynamics

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this series. The parameters of the bilinear system are determined by minimizing, in a statistical sense,the difference between the original system and the bilinear system. Application to a piecewise linear modelof a beam with a nonlinear one-sided supportillustrates the effectiveness of this approach in approximatingtruly nonlinear, stochastic response phenomena in both the statistical momentsand the power spectral density of the response of this system in case ofa white noise excitation.     

New bilinearization,Bäcklund transformation and infinite conservation laws for the KdV6 equation with Bell polynomials

By using the Bell polynomials method and symbolic computation, we study the integrability of the KdV6 equation. We develop, in this work, new results regarding the integrability concept. We show that the newly developed bilinear representation and bilinear Bäcklund transformation are different from those reported in the literature. Moreover, we firstly present the infinite conservation laws, and the conserved densities and fluxes are given in explicit recursion formulas. Copyright © 2015 John Wiley & Sons, Ltd.     

Different strategies for the direct determination of amoxicillin in human urine by second-order multivariate analysis of kinetic-spectrophotometric data

The kinetic evolution of UV-visible absorption spectra of amoxicillin in the presence of copper(II) ions has been processed by the second-order multivariate methods parallel factor analysis (PARAFAC) and also by a novel approach based on partial least-squares with residual bilinearization (PLS/RBL). The latter one is employed for the first time to evaluate kinetic-spectral information. The mechanism of the analyte metal-catalyzed hydrolysis involves a reaction intermediate and a final reaction product, both with spectra which may allow for the determination of amoxicillin in human urine, even in the presence of unsuspected sample components. This is possible thanks to the second-order advantage exploited by the employed chemometric algorithms, among which PARAFAC and PLS/RBL gave the best results. Amoxicillin was determined in a series of spiked and real urine samples, which allowed to perform, respectively, a recovery study and a comparison with the reference high-performance liquid chromatographic technique. The best figures of merit were obtained with PLS/RBL, namely sensitivity, 0.5 AU L mg⁻¹ (AU = absorbance units), analytical sensitivity, 500 L mg⁻¹ and limit of detection, 6 mg L⁻¹. Relative advantages and disadvantages of the employed algorithms are discussed.     

Room-temperature excitation-emission phosphorescence matrices and second-order multivariate calibration for the simultaneous determination of pyrene and benzo[a]pyrene

The present article describes the simultaneous phosphorimetric determination of pyrene and benzo[a]pyrene, two highly toxic polycyclic aromatic hydrocarbons, through excitation-emission phosphorescence matrices (EEPMs) and second-order calibration. The developed approach enabled us to determine both compounds at μg L⁻¹ concentration levels without the necessity of applying separation steps, as well as significantly reducing the experimental time. An artificial neural network (ANN) approach was applied to optimize the chemical variables which have an influence on the room-temperature phosphorescence emission of the studied analytes. The present study was employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The superior capability of PLS/RBL to model the profiles of other potentially interferent polycyclic aromatic hydrocarbons (PAHs) was demonstrated. The quality of the proposed method was established with the determination of both pyrene and benzo[a]pyrene in artificial and real water samples.     

Three-way partial least-squares/residual bilinearization study of second-order lanthanide-sensitized luminescence excitation-time decay data: analysis of benzoic acid in beverage samples

Lanthanide-sensitized luminescence excitation-time decay matrices were employed for achieving the second-order advantage using as chemometric algorithms parallel factor analysis (PARAFAC) and multidimensional partial least-squares with residual bilinearization (N-PLS/RBL). The second-order data were measured for a calibration set of samples containing the analyte benzoic acid in the concentration range from 0.00 to 5.00 mg L⁻¹, for a validation set containing the analyte and the potential interferent saccharin (in the range 0.00–6.00 mg L⁻¹), and for real samples of beverages containing benzoic acid as preservant, saccharin, and other potentially interfering compounds. All samples were treated with terbium(III), trioctylphosphine oxide as a synergistic ligand, and contained a suitable imidazol buffer, in order to ensure maximum intensity of the luminescence signals. The results indicate a slightly better predictive ability of the newly introduced N-PLS/RBL procedure over standard PARAFAC, both in what concerns the comparison with nominal analyte concentrations in the validation sample set and with results provided by the reference high-performance liquid chromatographic technique for the real sample set.     

Solutions and continuum limits to nonlocal discrete sine-Gordon equations: Bilinearization reduction method

In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, we construct exact solutions in double Casoratian form to the reduced nonlocal discrete sine-Gordon equations. Then, nonlocal semidiscrete sine-Gordon equations and their solutions are obtained through the continuum limits. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. The research ideas and methods in this paper can be generalized to other nonlocal discrete integrable systems.     

Improvement of residual bilinearization by particle swarm optimization for achieving the second‐order advantage with unfolded partial least‐squares

The combination of unfolded partial least‐squares (U‐PLS) with residual bilinearization (RBL) provides a second‐order multivariate calibration method capable of achieving the second‐order advantage. RBL is performed by varying the test sample scores in order to minimize the residues of a combined U‐PLS model for the calibrated components and a principal component model for the potential interferents. The sample scores are then employed to predict the analyte concentration, with regression coefficients taken from the calibration step. When the contribution of multiple potential interferents is severe, particle swarm optimization (PSO) helps in preventing RBL to be trapped by false minima, restoring its predictive ability and making it comparable to the standard parallel factor (PARAFAC) analysis. Both simulated and experimental systems are analyzed in order to show the potentiality of the new technique. Copyright © 2007 John Wiley & Sons, Ltd.