In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to have an excellent performance: it deviates from numerically exact calculations by less than 0.15% for a vast regime of interactions and for all the regimes of filling factors and magnetizations. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, ~7%, against only ~0.1% for the neural network. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.

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A compilation of papers published between 2014 and 2018 was evaluated. Many papers related to multivariate calibration and classification have been reported, as well as, design of experiments applications and artificial intelligence methods. Some applications were highlighted, as medical and pharmaceutical, food analysis, fuels, biological and forensic for the chemometric techniques on this review. Most studies are related to developing methods for practical solutions in industry or routine analysis. A promising scenario is shown considering the number of published papers: a total of 832 for this period using the keywords, multivariate classification, multivariate calibration, analysis, chemometrics, prediction, analytical chemistry, artificial neural networks (ANN), design of experiments (DoE) and factorial design. An useful overview for Analytical Chemistry researchers´ combined with Chemometrics is presented in this review.

Dry grains from leguminous species, such as soybeans (Glycine max L.), common beans (Phaseolus vulgaris L.), chickpeas (Cicer arietinum L.) and corn (Zea mays L.), are regularly consumed for human nutrition. This paper showed the possibility of estimating bulk density as quality parameter of 4 different dry grains (soybeans, common beans, chickpeas and corn) in a same model using the average values of color descriptors from digital images combined with an artificial neural network, with low computational costs. These food products are good sources of carbohydrates, protein and dietary fiber, and they possess significant amounts of vitamins and minerals and a high energetic value. Estimation of the physicochemical properties of grains is challenging due to variations in shape, texture, and size and because the grain colors appear similar to the naked eye. In this work, an analytical method was developed based on digital images converted into ten color scale descriptors combined with a neural model to provide an accurate parameter for grain quality control with a low computational cost. The bulk densities of four type of grains, i.e., soybeans, beans, chickpeas and corn, were predicted using numerical data represented by the average values of color histograms of a ten color scale (red - R, green - G, blue - B, hue - H, saturation - S, value - V, relative RGB and luminosity - L) from digital images combined with artificial neural networks (ANNs). The reference bulk densities were empirically measured. A very good correlation between the reference values and values predicted by the ANN was achieved, and with a single ANN developed for the four grains, a correlation coefficient of 0.98 was observed for the test set. Moreover, the relative errors were between 0.01 and 5.6% for the test set.

Introduction: The mechanical competence parameter (MCP) of the trabecular bone is a parameter that merges the volume fraction, connectivity, tortuosity and Young modulus of elasticity, to provide a single measure of the trabecular bone structural quality. Methods: As the MCP is estimated for 3D images and the Young modulus simulations are quite consuming, in this paper, an alternative approach to estimate the MCP based on artificial neural network (ANN) is discussed considering as the training set a group of 23 in vitro vertebrae and 12 distal radius samples obtained by microcomputed tomography (μCT), and 83 in vivo distal radius magnetic resonance image samples (MRI). Results: It is shown that the ANN was able to predict with very high accuracy the MCP for 29 new samples, being 6 vertebrae and 3 distal radius bones by μCT and 20 distal radius bone by MRI. Conclusion: There is a strong correlation (R 2 = 0.97) between both techniques and, despite the small number of testing samples, the Bland-Altman analysis shows that ANN is within the limits of agreement to estimate the MCP.