RESUMEN
BACKGROUND: Various classification, class modeling, and clustering techniques operate within abstract spaces, utilizing Principal Components (e.g., Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA)) or latent variable spaces (e.g., Partial Least Squares Discriminant Analysis (PLS-DA)). It's important to note that PCA, despite being a mathematical tool, defines its Principal Components under certain mathematical constraints, it has a wide range of applications in the analysis of real-world systems. In this research, we assess the viability of employing the Multivariate Curve Resolution (MCR) subspace within class modeling techniques, as an alternative to the PC subspace. (92). RESULTS: This study evaluates the use of the MCR subspace in class modeling methods, specifically in tandem with soft independent modeling of class analogy (SIMCA), to investigate the advantages of employing the meaningful physico-chemical subspace of MCR over the mathematical subspace of PCA. In the MCR-SIMCA strategy, the model is constructed by applying MCR to training samples from a target class. The MCR model effectively partitions the data into two smaller sub-matrices: the contribution matrix and the corresponding response matrix. In the next step, the contribution matrix resulting from the decomposition of the training set develops a distance plot (DP). First, the theory of the MCR-SIMCA model is discussed in detail. Next, two real experimental datasets were analyzed, and their performance was compared with the DD-SIMCA model. In most cases, the results were as good as or even more satisfactory than those obtained with the DD-SIMCA model. (146). SIGNIFICANCE: The suggested class modeling method presents a promising avenue for the analysis of real-world natural systems. The study's results emphasize the practical utility of the MCR approach, underscoring the significance of the MCR subspace advantages over the PCA subspace. (39).
RESUMEN
Multivariate self-modeling curve resolution (SMCR) methods are the best choice for analyzing chemical data when there is not any prior knowledge about the chemical or physical model of the process under investigation [[1Q3: The reference '1' is only cited in the abstract and not in the text. Please introduce a citation in the text.]]. However, the rotational ambiguity is the main problem of SMCR methods, yielding a range of feasible solutions. It is, therefore, important to determine the range of all feasible solutions of SMCR methods. Different methods have been presented in the literature to find feasible solutions of two, three, and four component systems. Here, a novel simple SMCR method is presented for calculating the boundaries of feasible solutions of two-component systems. At first, the simple strategy is presented for calculating the feasible solutions of two-component systems. Next, four different experimental two-component systems are analyzed in detail for calculating the boundaries of feasible solutions in both spaces, including complex formation equilibrium, keto-enol tautomerization kinetic, lipidomics data, and a case for quantification of an analyte in gray systems. In all cases, the boundaries of range of feasible solutions are properly determined by the proposed simple strategy.
RESUMEN
A novel strategy for calibrating Indicator Displacement Assay (IDA)-based sensors is presented herein. The main idea is to replace the instrumental measurement responses by the equilibrium concentration of spectroscopically active species which can be obtained by the Classical Least Squares (CLS) method. Also, coupling the Indirect Hard Modelling (IHM) and CLS methods for the calibration model resulted in a reduction of matrix effects. According to Beer's law, the measured multivariate spectrum of a mixture is the sum of contributions of all spectroscopically active components via their concentrations and pure spectra. Concentrations of a few components are usually the fundamental variables in a measured spectrum in several sensors or wavelengths. In IDA systems, the equilibrium concentrations of indicator and indicator-receptor species are the fundamental variables that can be an alternative for instrumental responses as the input data for regression methods. These fundamental variables can be exploited from the recorded spectra of the mixtures when the pure spectra of the active species are known. Using dramatically reduced number of input variables without the need for any variable selection method is the main advantage of this idea over conventional calibration methods that use variable selected spectroscopic signals. This strategy can be applied for systems in which the active species are known. Accordingly, for IDA-based sensors with determined pure response to indicator and indicator-receptor complex, the free concentrations of active species can be resolved by the Classical Least Squares (CLS) method. The pure analytical responses are altered in mixtures due to the intermolecular interactions caused by matrix effect in real experimental dataset. So, the free concentrations of spectroscopically active species are not resolved correctly by the CLS method. To tackle the issue of nonlinearity of data due to the matrix effect, the Indirect Hard Modelling (IHM) can be applied to correctly resolve the fundamental variables. The applicability of the presented idea is successfully validated by simulated and real sensor array systems.
RESUMEN
The discrepancy between concentrations and activities is a predicament well known to the analytical chemist. Because of the difficulty of determining activity coefficients, the standard technique for quantitative equilibrium studies is to work under a particular 'constant ionic strength' by adding an excess of an inert salt. Under such conditions, activity coefficients are approximately constant and can be taken into the equilibrium constants which are defined for the chosen ionic strength (I). Here we propose a fundamentally different approach. Throughout the numerical analysis of the titration data, activity coefficients for all individual species are approximated by well-known equations based on the work of Debye-Hückel. The computational analysis of the measurements strictly obeys the law of mass conservation and obeys the law of mass action only approximately. The main novelty is that now the addition of inert salts is no longer required and measurements are done at minimal I. Consequently, the thermodynamic equilibrium constants are now determined much more robustly based on experiments taken at low I. The approach has been tested and validated with the two very well investigated 3-protic phosphoric and citric acids. In summary: the technique of artificially keeping ionic strength constant has been replaced by improved computational analysis.
