A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

A polarographic study of Cd(II)-NTA complexes in alkaline solution

Up to four d.c. polarographic waves were observed on voltammetric curves of Cd(II)-nitrilotriacetate complexes on the DME in the pH range 7.0–11.5. These polarograms are analyzed using a non-linear least squares method and the mechanism of the electrode reactions and prior homogeneous reaction are discussed. The kinetic parameters of the separate reactions are calculated and compared with literature values. The accelerating influence of OH^? ions on the dissociation of the complexes is established.     

Prozentuales und logarithmisches Verfahren zur Berechnung von Eichkurven

Two methods, one on the basis of percent and another on the basis of logarithm, for the calculation of calibration curves are reported. By these procedures the lower values of the calibration curves are represented more strongly than by the normal method of the least sum of error squares. Instead of the coefficient of correlation a coefficient of quality is defined, to characterize the quality of the calibration curves. The coefficient of quality is calculated from the percentage deviations of the calculated x-values in the way of the standard deviation.     

动力学过程的精确模拟

采用加权最小二乘法更精确地模拟了化学动力学过程,结出了几种常见动力学模型的权重函数。用普通最小二乘法和加权最小二乘法对聚时苯二甲酸乙二酯的结晶动力学过程进行了处理。方差分析表明,两种加权最小二乘法的标准差均小于普通最小二乘法的标准差,所得斜率和截距也有明显不同,示出了模拟的相对结晶度及其导数曲线。     

Sensitive and selective cocaine electrochemical detection using disposable sensors

This paper describes the voltammetric determination of cocaine in presence of three different interferences that could be found in street samples using disposable sensors. The electrochemical analysis of this alkaloid can be affected by the presence of codeine, paracetamol or caffeine, whose oxidation peaks may overlap and lead to false positives. This work describes two different solutions to this problem. On one hand, the modification of disposable carbon sensors with carbon nanotubes allows the voltammetric quantification of cocaine by using ordinary least squares regressions in the concentration range from 10 to 155 μmol L⁻¹, with a reproducibility of 5.6% (RSD, n = 7. On the other hand, partial least squares regressions are used for the resolution of the overlapped voltammetric signals when using screen-printed carbon electrodes without any modification. Both procedures have been successfully applied to the evaluation of the purity of cocaine street samples.     

The determination of the equilibrium geometry of a molecule with the use of microwave data and theoretical rotational-vibrational interaction constants

The applicability of the classic method for calculating the equilibrium structure (r _e) of a polyatomic molecule with the use of experimental rotational constants and rotational-vibrational interaction constants (α _r ^B ) is considered. Direct minimization of the nonlinear functional of the sum of the squares of discrepancies by the Broyden-Fletcher-Goldfarb-Shanno method is suggested. Statistical parameters (confidence intervals and correlation coefficients) can be calculated by the double numerical differentiation of this functional. If the problem is ill-conditioned or some data are lacking, the Tychonoff regularization method can be used. The effectiveness of the suggested approach is demonstrated for the example of two molecules (cyclopropene and 3,3-difluorocyclopropene).     

Local classification: Locally weighted–partial least squares-discriminant analysis (LW–PLS-DA)

The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW–PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones.     

Calibration graphs in isotope dilution mass spectrometry

Isotope-based quantitation is routinely employed in chemical measurements. Whereas most analysts seek for methods with linear theoretical response functions, a unique feature that distinguishes isotope dilution from many other analytical methods is the inherent possibility for a nonlinear theoretical response curve. Most implementations of isotope dilution calibration today either eliminate the nonlinearity by employing internal standards with markedly different molecular weight or they employ empirical polynomial fits. Here we show that the exact curvature of any isotope dilution curve can be obtained from three-parameter rational function, y = f(q) = (a₀ + a₁q)/(1 + a₂q), known as the Padé[1,1] approximant. The use of this function allows eliminating an unnecessary source of error in isotope dilution analysis when faced with nonlinear calibration curves. In addition, fitting with Padé model can be done using linear least squares.     

Deconvolution of multicomponent ultraviolet/visible spectra

A reliable method based on non-negative least squares is suggested for the deconvolution of spectra of chemical and biochemical mixtures into their individual components. The efficiency of the method is demonstrated by use of artificial inorganic salt mixtures of defined composition as well as of real carotenoid samples of considerable complexity, the results for which are compared with those of conventional chromatography. The problem of error propagation is discussed and compared to the sensitivity of standard least-squares and n-wavelengths algorithms.     

Predictive-property-ranked variable reduction in partial least squares modelling with final complexity adapted models: Comparison of properties for ranking

The calibration performance of partial least squares regression for one response (PLS1) can be improved by eliminating uninformative variables. Many variable-reduction methods are based on so-called predictor-variable properties or predictive properties, which are functions of various PLS-model parameters, and which may change during the steps of the variable-reduction process. Recently, a new predictive-property-ranked variable reduction method with final complexity adapted models, denoted as PPRVR-FCAM or simply FCAM, was introduced. It is a backward variable elimination method applied on the predictive-property-ranked variables. The variable number is first reduced, with constant PLS1 model complexity A, until A variables remain, followed by a further decrease in PLS complexity, allowing the final selection of small numbers of variables.     

New MSPQC-PLS method for the early clinic identification of commonly encountered Candida species

The early clinic identification of commonly encountered Candida species became more important with the increasing human candidiasis. In this paper, a new MSPQC-PLS (multi-channel series piezoelectric quartz crystal biosensor combined with partial least square) method was proposed for early identification of the most frequent Candida species encountered in human pathology. This method was based on these fact that (1) MSPQC method is a real-time monitoring method based on the sensitive frequency response to the change of electric parameters of the culture media caused by the growth of microorganisms; (2) various Candida species produce significantly different types of frequency curves in 1 or 2 days’ culture period; (3) this difference can be identified by the partial least square technique. Using the proposed method, three species (Candida albicans, Candida glabrata, and Candida tropicalis) from a collection of 53 clinical strains of Candida, isolated from hospitalized patients, were identified with a classification rate of 98.1%. New proposed MSPQC-PLS method is simple, rapid and convenient to perform. It can identify clinical Candida species directly without passing through pure culture process. This will save identification time greatly. It could be popularized in clinical microbiology laboratories.     

Combinative neural network and its applications

A new approach named combinative neural network (CN) using partial least squares (PLS) analysis to modify the hidden layer in the multi-layered feed forward (MLFF) neural networks (NN) was proposed in this paper. The significant contributions of PLS in the proposed CN are to reorganize the outputs of hidden nodes such that the correlation of variables could be circumvented, to make the network meet the non-linear relationship best between the input and output data of the NN, and to eliminate the risk of over-fitting problem at the same time. The performance of the proposed approach was demonstrated through two examples, a well defined nonlinear approximation problem, and a practical nonlinear pattern classification problem with unknown relationship between the input and output data. The results were compared with those by conventional MLFF NNs. Good performance and time-saving implementation make the proposed method an attractive approach for non-linear mapping and classification.     

Errors in parameters extracted from A exp(—kt) + Z data and effects of not weighting the data

Earlier work is extended by providing relative standard deviations (σ) for the background (Z) and the pre-exponential factor (A) via analysis of 2400 simulated decays for various decade ranges, Z/A and kinds of error using weighted non-linear least squares (WNLLS), the method yielding the lowest relative standard deviation of the rate constant. These σ enable experimenters to make more objective and quantitative assessments of the relative worth of extending, for example, the time over which data are collected to get more precise parameters. Effects of ignoring relative weights in the analyses are also examined. Their omission yields σ derived from the fit that are unreliable. Moreover, the σ² calculated from the sets of parameters extracted from many simulated decays are sometimes more than doubled. Efficiency [ = σ² (weighted)/σ² (not weighted)] is then halved: this amounts to ignoring half the data that has required time, effort and resources to collect.     

Application of non-linear regression methods for the estimation of common kinetic parameters from several thermoanalytical curves

Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m?T) or DTG (dm/dt-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO₃ in open crucible. In these cases the Arrhenius terms and then-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S _res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.     

Comparison of several background compensation methods useful for evaluation of energy-dispersive X-ray fluorescence spectra

A number of background estimation and modelling strategies suitable for evaluating energy-dispersive X-ray spectra by means of non-linear least squares fitting are evaluated and intercompared. As background modelling functions, exponential and linear combinations of mutually orthogonal polynomials are considered. These functions allow the shape of the background to be determined together with the photopeak intensities. As background estimation algorithms, an iterative stripping algorithm and a background channel selection procedure which is also based on the use of orthogonal polynomials are studied. The last two methods calculate the spectral background prior to the actual fitting process. For the intercomparison, the various methods were incorporated in the software package AXIL (Analysis of X-ray spectra by means of Iterative Least Squares). By using simulated spectra in which the intensity of all lines is a priori known, the accuracy and noise-sensitivity of the different background compensation strategies are evaluated. The method in which the background is modelled as a linear combination of orthogonal polynomials is identified as being the most robust and yielding the most accurate results.     

Polarographic studies on the electrode kinetics of the nickel(II) complexes with glycine and some of its derivatives: I. glycine complexes

D.C. polarograms of the Ni(II)-glycine complexes were measured with varying pH values at constant total glycine concentration (0.05 M) and conversely with varying total glycine concentration at constant pH values (3.5, 4.5, 7.5 and 9.5). The current—voltage curves obtained were analysed to determine the limiting currents, the transfer coefficients, and the half-wave potentials, by using the non-linear least squares method. From the dependence of the half-wave potentials on the free glycine concentration, the mechanism of the electrode processes was elucidated. It was shown that the first wave corresponded to the reduction of the Ni²⁺ aquo-complex, the second to the NiG⁺ complex, the third to the NiG₂ complex and the fourth to the NiG^?₃ complex. The kinetic parameters for the four charge transfer processes were determined.The second and third waves were kinetic in character and the rate constants of the dissociation and association reactions between NiG⁺ and NiG₂ and between NiG₂ and NiG^?₃ were determined by analysing the dependence of the kinetic limiting currents on the free glycine concentration.     

Establishment of multivariate specifications for food commodities with discriminant partial least squares

A novel method for establishing multivariate specifications of food commodities is proposed. The specifications are established for discriminant partial least squares (DPLS) by setting limits on the predictions of the DPLS model together with Hotelling T² and square error of prediction (SPE). These limits can be tuned depending on whether type I error (i.e. a correct sample is declared out-of-specification) or type II error (i.e. an out-of-specification sample is declared within specifications) need to be minimized. The methodology is illustrated with a set of NIR spectra of Italian olive oils, corresponding to five regions and the class Liguria is the class of interest. The results demonstrate the possibility of establishing multivariate specification for olive oils from the Liguria region on the basis of spectral data obtaining type I and type II errors lower than 5%.     

Fluorescence spectroscopic determination of triglyceride in human serum with window genetic algorithm partial least squares

Fluorescence spectrum, as well as the first and second derivative spectra in the region of 220–900 nm, was utilized to determine the concentration of triglyceride in human serum. Nonlinear partial least squares regression with cubic B‐spline‐function‐based nonlinear transformation was employed as the chemometric method. Window genetic algorithms partial least squares (WGAPLS) was proposed as a new wavelength selection method to find the optimized spectra wavelengths combination. Study shows that when WGAPLS is applied within the optimized regions ascertained by changeable size moving window partial least squares (CSMWPLS) or searching combination moving window partial least squares (SCMWPLS), the calibration and prediction performance of the model can be further improved at a reasonable latent variable number. SCMWPLS should start from the sub‐region found by CSMWPLS with the smallest root mean squares error of calibration (RMSEC). In addition, WGAPLS should be utilized within the region of smallest RMSEC whether it is the sub‐region found by CSMWPLS or region combination found by SCMWPLS. Moreover, the prediction ability of nonlinear models was better than the linear models significantly. The prediction performance of the three spectra was in the following order: second derivative spectrum < original spectrum < first derivative spectrum. Wavelengths within the region of 300–367 nm and 386–392 nm in the first derivative of the original fluorescence spectrum were the optimized wavelength combination for the prediction model. Copyright © 2012 John Wiley & Sons, Ltd.