Partial least-squares modelling of dye fastness to light

Several physicochemical properties (¹³C-n.m.r., spectrophotometric, chromatographic, calorimetric) were measured for a series of 38 azo dyes in order to test the existence of relationships between one or more of these data sets and the fastness of the dyes on polyester fabric. The partial least-squares method was applied; it had previously proved useful in establishing structure/property relationships for the same dyes. It is shown that ¹³C-n.m.r. data can be used successfully to predict dye fastness to light. These data are quickly and cheaply obtained with small amounts of compound.     

Partial least-squares regression on design variables as an alternative to analysis of variance

The partial least-squares (PLS) algorithm has become popular for explorative multivariate data analysis and for multivariate calibration. The same PLS algorithm can also be used for confirmatory data analysis. The discussion is limited to analysis of a single response variable. A close correspondence of PLS1 regression to classical analysis of variance (ANOVA) is demonstrated. The design of an experiment is described in terms of discrete design variables for main effects and simple interactions (dummy variables). These are used as regressors X = (x₁, x₂,…,) for modelling the response variable of the experiment, y. As in conventional use of PLS1 regression, the algorithm gives a concentrated model or diagram of the most important, y-relevant variability types in the X-data. In the present case, this gives the combination of design variables that models the variations in y. A simple plot of the resulting factor loadings immediately reveals the important design variables. Statistical tests and confidence regions in the PLS solution give additional safeguards against interpretation of spurious effects. The method is applied to two data sets. One concerns assessment of personal preference for blackcurrent juice, studied in a 2⁵ factorial experiment; these data are also studied with missing values and as fractional factorials. The other ceoncers spectrophotometric absorbance-based colour assessments of pigment in strawberry jam in a 3-factor design with 2, 2 and 3 levels in the respective factors.     

Partial least-squares regression: a tutorial

A tutorial on the partial least-squares (PLS) regression method is provided. Weak points in some other regression methods are outlined and PLS is developed as a remedy for those weaknesses. An algorithm for a predictive PLS and some practical hints for its use are given.     

Partial least-squares modeling of continuous nodes in Bayesian networks

In Bayesian networks it is necessary to compute relationships between continuous nodes. The standard Bayesian network methodology represents this dependency with a linear regression model whose parameters are estimated by a maximum likelihood (ML) calculation. Partial least-squares (PLS) is proposed as an alternative method for computing the model parameters. This new hybrid method is termed PLS-Bayes, as it uses PLS to calculate regression vectors for a Bayesian network. This alternative approach requires storing the raw data matrix rather than sequentially updating sufficient statistics, but results in a regression matrix that predicts with higher accuracy, requires less training data, and performs well in large networks.     

Partial least-squares regression and fuzzy clustering — A joint approach

Chemical and physical analyses of malt, the main ingredient of beer, have been used to predict the concentration of certain volatile compounds in the finished beer.The prediction was done by means of the partial least squares regression (PLS2) in SIMCA. The total data set as well as individual malt clusters were submitted to PLS analysis. Best prediction was obtained by separating the total object matrix in classes according to similarity found by fuzzy pattern recognition (FCV). FCV was also used to separate the beer variables in classes and to select the subset of variables to be predicted.A joint approach of fuzzy pattern recognition to identify groups of samples and SIMCA-PLS2 to predict several dependent variables is suggested as a powerful tool in process-analytical chemistry.     

Non-linear least-squares fitting with microsoft excel solver and related routines in HPLC modelling of retention

Summary Two problems related to non-linear regression, the evaluation of the best set of fitting parameters and the reliability of the methods used for the estimation of the standard errors of these parameters, are examined. It is shown that a non-linear curve fitting routine, like the Microsoft Excel Solver, may give more than one solution for the same data set and a simple Monte Carlo routine is described for the evaluation of the bestfit. For standard errors, the reliability of two procedures based on the conventional curvature matrix method, four Jackknife techniques and the bootstrap method are examined by comparing their results to those obtained from a Monte Carlo simulation of the experimental data. It is shown that a fitting parameter may follow a nonnormal distribution when the equation to be fitted is complicated, even if the errors on the data are normally distributed. In this case only Monte Carlo methods of data simulation can give accurate information about the standard errors and the confidence intervals of these parameters.     

Application of partial least-squares modelling in the optimization of a waste-water treatment plant

The partial least-squares method was applied to data collected at a municipal waste-water treatment plant to estimate the relationship between the process parameters and effluent quality. The main reason for poor treatment efficiency was the so-called bulking phenomemon of the activated sludge. The PLS model of the data presenting a normal period of operation and the bulking period thereafter showed that high temperature and decreasing concentrations of carbon and phosphorus contributed to the bulking state.     

Information content of data and variables and types of weighting in least-squares regression methods

Algorithms are given for evaluating the relative amount of useful information related to a particular parameter which is carried by individual data points and intervals of the variables. The algorithms provide an efficient means of using the information contained in a set of data. Applications to the optimization of weighting in regression methods are described. Several informational and combined informational-statistical types of weighting are studied as a means of improving the accuracy and precision of the parameters obtained by non-linear regression.     

Independent component analysis yields chemically interpretable latent variables in multivariate regression

This work shows that independent component analysis (ICA) can be used to obtain statistically independent and, therefore, chemically interpretable latent variables (LVs) in multivariate regression. Two novel algorithms based on ICA are introduced and compared with two classical methods on simulated data: principal component regression and partial least-squares regression. All methods compared yield accurate predictions, but only those based on ICA yield LVs that are chemically interpretable. Practical limitations of ICA-based regression with respect to the underlying assumptions, sample size, and measurement noise are discussed and illustrated by means of simulations.     

Liver functional magnetic resonance imaging analysis using a latent variables approach

The liver is a highly vascular organ with a dual blood supply, and it performs a remarkable number of vital functions. Here, we show, through measurement of blood oxygen level‐dependent (BOLD) signal, that liver arterial and hepatic portal blood supplies can be modulated through hyperoxia exposure and by consumption of a standardized meal, respectively. As such, we suggest that hyperoxia modulates the hepatic arterial BOLD signal, whereas a controlled meal changes predominantly the hepatic portal BOLD signal. The hemodynamics of the dual liver blood supplies in response to the aforementioned challenges are complex and variable across subjects, making a general linear model‐based analysis difficult. Therefore, we present the application of two local (at each voxel) hemodynamic response‐independent techniques—principal component analysis and partial least squares—to observe the hypothesized reduction in BOLD contrast during cycles of hyperoxic breathing, when comparing preprandial versus postprandial states in a normally functioning liver. We illustrate the ability of our techniques to differentiate between healthy and diseased livers with an analysis of 17 subjects—11 with normal livers and 6 with liver disease (hepatitis or cirrhosis). Our local analysis can correctly classify all of the subjects. Copyright © 2012 John Wiley & Sons, Ltd.     

Partial least-squares near-infrared determination of hydrocarbons removed from polluted waters by using tanned solid wastes

A new procedure has been developed for the determination of hydrocarbons retained in solid tanned wastes from polluted waters. The method uses near-infrared (NIR) transmission spectra obtained from leachates of the hydrocarbons with CCl₄ using a partial least-squares (PLS) calibration model based on the use of mixtures of n-hexane, isooctane, and toluene diluted with CCl₄. This methodology was applied to the evaluation of the absorption capacity of chrome shavings in water samples polluted with hydrocarbons, resulting in a maximum absorption capacity of 6.30 g hydrocarbons per g solid waste.     

Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly constrains the electronic Cartesian coordinates to the physical subspace of the mapping. We numerically demonstrate that the resulting PI-ST representation is exact for the calculation of equilibrium properties of systems with coupled electronic and nuclear degrees of freedom. We further show that the PI-ST formulation provides a natural means to initialize semiclassical trajectories for the calculation of real-time thermal correlation functions, which is numerically demonstrated in applications to a series of nonadiabatic model systems.     

Partial multifactorial design in modelling of UV-spectrometric assays of ascorbic acid with nitrosobenzene and p-nitro-nitrosobenzene

Two new reagents, nitrosobenzene (PhNO) and p-nitro-nitrosobenzene (p-NO2-PhNO), have been studied for the analysis of ascorbic acid (AA) by its hypochromic effect on the reagents. The partial multifactorial design of experiments coupled with analysis of parallelism of calibration lines was used to optimize the experimental conditions and evaluate the parameters which affect the sensitivity and accuracy. Two levels at which variable parameters are to be examined should be chosen carefully if a single-step examination is expected to be sufficient. If any parameter roughly influences the system it results not only in severe rotational and translational effects, but also in false results and low selectivity of the approach. In such a case a second step of examination is necessary. The optimization procedures indicated that both PhNO and p-NO2-PhNO are advantageous analytical reagents for the UV-spectrometric assay of AA at pH 3 when measuring the decrease of the absorbance of the reagent peak as analytical signal after 10 and 1 min, resp. After proper modelling both systems were sufficiently robust to be successfully applied for accurate, selective, sensitive, precise and simple analyses of AA even in pharmaceutical preparations with acetylsalicylic acid. Respective analytical performances characterizing AA-PhNO and AA-p-NO2-PhNO systems were: linearity range 2-100 and 2-70 micromol L(-1), CS 0.0094 and 0.0115 L micromol(-1), accuracy 101.5 and 98.0%, LOQ 1.3-2.1 and 3.1-3.6 micromol L(-1) and RSD 1.3-3.5 and 1.9-3.8%.     

Partial least-squares regression for the simultaneous determination of aluminum and beryllium in geochemical samples using xylenol orange

A partial least-squares regression (PLS) was developed for the simultaneous spectrophotometric determination of aluminum and beryllium in geochemical samples by xylenol orange as the chromogenic reagent in water media and in micellar media. The effects of pH, xylenol orange concentration and surfactant concentration on the complexes formation reactions were studied. In the absence of surfactant the complex color development takes place at 2 h after mixing the reagents. By using CTAB as micellar media the complexes formation was improved and the rate of the complexation reactions increased. By using PLS-1 algorithm satisfactory results were obtained. The proposed procedure showed to be useful for prediction of Al and Be values from 0.1 to 1.0 mg L(-1).     

On the frequency-dependent specific heat and TMDSC: Constitutive modelling based on thermodynamics with internal state variables

To develop constitutive models to represent the thermomechanically chemically coupled behaviour of curing resins, vulcanizing elastomers or melting and crystallizing polymers the technique of DSC is extremely helpful. In the present study, the method of TMDSC is interpreted and evaluated in the context of thermodynamics with internal state variables. The balance equation of energy and the dissipation principle in the form of the Clausius–Duhem inequality form the theoretical basis of our study. Since the pressure and the temperature are the external variables in DSC, the specific Gibbs free energy is used as thermodynamic potential. It depends on temperature, stress and a set of internal state variables to represent the microstructure of the material on a phenomenological basis. The temperature- and internal variable-induced changes in the Gibbs free energy are approximated by a Taylor series up to second order terms. As a substantial result of this work, closed-form expressions for the dynamic calorimetric response due to harmonic temperature perturbations and the frequency-dependent complex heat capacity are derived. The theory allows a physical interpretation of the complex heat capacity and its underlying phenomena and is in accordance with experimental observations from literature.     

Partial least-squares with residual bilinearization for the spectrofluorimetric determination of pesticides. A solution of the problems of inner-filter effects and matrix interferents

This paper demonstrates for the first time the power of a chemometric second-order algorithm for predicting, in a simple way and using spectrofluorimetric data, the concentration of analytes in the presence of both the inner-filter effect and unsuspected species. The simultaneous determination of the systemic fungicides carbendazim and thiabendazole was achieved and 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 chemometric study was performed using fluorescence excitation-emission matrices obtained after the extraction of the analytes over a C18-membrane surface. The ability of PLS/RBL to recognize and overcome the significant changes produced by thiabendazole in both the excitation and emission spectra of carbendazim is demonstrated. The high performance of the selected PLS/RBL method was established with the determination of both pesticides in artificial and real samples.     

Optimal designs with information theory in least-squares problems

The application of information theory in a recursive least-squares context is described. A theoretical discussion of the method is presented and its suitability for the optimal design problem is discussed. The resulting algorithms are simple, fast and easy to implement on a computer and may be used either in an on-line or an off-line fashion.