Green Multi-Platform Solution for the Quantification of Levodopa Enantiomeric Excess in Solid-State Mixtures for Pharmacological Formulations

The aim of the present work was to develop a green multi-platform methodology for the quantification of l-DOPA in solid-state mixtures by means of MIR and NIR spectroscopy. In order to achieve this goal, 33 mixtures of racemic and pure l-DOPA were prepared and analyzed. Once spectra were collected, partial least squares (PLS) was exploited to individually model the two different data blocks. Additionally, three different multi-block approaches (mid-level data fusion, sequential and orthogonalized partial least squares, and sequential and orthogonalized covariance selection) were used in order to simultaneously handle data from the different platforms. The outcome of the chemometric analysis highlighted the quantification of the enantiomeric excess of l-DOPA in enantiomeric mixtures in the solid state, which was possible by coupling NIR and PLS, and, to a lesser extent, by using MIR. The multi-platform approach provided a higher accuracy than the individual block analysis, indicating that the association of MIR and NIR spectral data, especially by means of SO-PLS, represents a valid solution for the quantification of the l-DOPA excess in enantiomeric mixtures.

An Inexact Penalty Decomposition Method for Sparse Optimization

The penalty decomposition method is an effective and versatile method for sparse optimization and has been successfully applied to solve compressed sensing, sparse logistic regression, sparse inverse covariance selection, low rank minimization, image restoration, and so on. With increase in the penalty parameters, a sequence of penalty subproblems required being solved by the penalty decomposition method may be time consuming. In this paper, an acceleration of the penalty decomposition method is proposed for the sparse optimization problem. For each penalty parameter, this method just finds some inexact solutions to those subproblems. Computational experiments on a number of test instances demonstrate the effectiveness and efficiency of the proposed method in accurately generating sparse and redundant representations of one-dimensional random signals.

Multiblock Analysis Applied to TD-NMR of Butters and Related Products

This work presents a novel and rapid approach to predict fat content in butter products based on nuclear magnetic resonance longitudinal (T1) relaxation measurements and multi-block chemometric methods. The potential of using simultaneously liquid (T1L) and solid phase (T1S) signals of fifty samples of margarine, butter and concentrated fat by Sequential and Orthogonalized Partial Least Squares (SO-PLS) and Sequential and Orthogonalized Selective Covariance Selection (SO-CovSel) methods was investigated. The two signals (T1L and T1S) were also used separately with PLS and CovSel regressions. The models were compared in term of prediction errors (RMSEP) and repeatability error (σrep). The results obtained from liquid phase (RMSEP ≈ 1.33% and σrep≈ 0.73%) are better than those obtained with solid phase (RMSEP ≈ 5.27% and σrep≈ 0.69%). Multiblock methodologies present better performance (RMSEP ≈ 1.00% and σrep≈ 0.47%) and illustrate their power in the quantitative analysis of butter products. Moreover, SO-Covsel results allow for proposing a measurement protocol based on a limited number of NMR acquisitions, which opens a new way to quantify fat content in butter products with reduced analysis times.

The Quality of the Covariance Selection through Detection Problem and AUC Bounds

This paper considers the problem of quantifying the quality of a model selection problem for a graphical model. The model selection problem often uses a distance measure such as the Kulback-Leibler (KL) distance to quantify the quality of the approximation between the original distribution and the model distribution. We extend this work by formulating the problem as a detection problem between the original distribution and the model distribution. In particular, we focus on the covariance selection problem by Dempster, [1], and consider the cases where the distributions are Gaussian distributions. Previous work showed that if the approximation model is a tree, that the optimal tree that minimizes the KL divergence can be found by using the Chow-Liu algorithm [2]. While the algorithm minimizes the KL divergence it does not minimize other measures such as other divergences and the area under the curve (AUC). These measures all depend on the eigenvalues of the correlation approximation measure (CAM). We find expressions for KL divergence, log-likelihood ratio, and AUC as a function of the CAM. Easily computable upper and lower bounds are also found for the AUC. The paper concludes by computing these measures for real and synthetic simulation data.