Betanin and betanidin are compounds with extensive interest; they are effectively free radical scavengers. The present work aims to elucidate the differences between the mechanism of the antioxidant activity of betanin, betanidin, and their respective C15-epimers. Shape Theory establishes comparisons between the molecules’ geometries and determines parallelisms with the descriptors BDE, PA, ETE IP, PDE, and infrared spectra (IR) obtained from the molecule simulations. Furthermore, the molecules were optimized using the B3LYP/6-31+G(d,p) protocol. Finally, the molecular docking technique analyzes the antioxidant activity of the compounds in the complex with the therapeutic target xanthine oxidase (XO), based on a new proposal for the geometrical arrangement of the ligand atoms in the framework of Shape Theory. The results obtained indicate that the SPLET mechanism is the most favorable in all the molecules studied and that the first group that loses the hydrogen atom in the four molecules is the C17COOH, presenting less PA the isobetanidin. Furthermore, regarding the molecular docking, the interactions of these compounds with the target were favorable, standing out to a greater extent the interactions of isobetanidin with XO, which were analyzed after applying molecular dynamics.

Diverse phenomena from the real-world can be modeled using random matrices, allowing matrix-variate distributions to be considered. The normal distribution is often employed in this modeling, but usually the mentioned random matrices do not follow such a distribution. An asymmetric non-normal model that is receiving considerable attention due to its good properties is the Birnbaum–Saunders (BS) distribution. We propose a statistical methodology based on matrix-variate BS distributions. This methodology is implemented in the statistical software R. A simulation study is conducted to evaluate its performance. Finally, an application with real-world matrix-variate data is carried out to illustrate its potentiality and suitability.

This paper proposes a validation-comparison method for burned area (BA) products. The technique considers: (1) bootstrapping of scenes for validation-comparison and (2) permutation tests for validation. The research focuses on the tropical regions of Northern Hemisphere South America and Northern Hemisphere Africa and studies the accuracy of the BA products: MCD45, MCD64C5.1, MCD64C6, Fire CCI C4.1, and Fire CCI C5.0. The first and second parts consider methods based on random matrix theory for zone differentiation and multiple ancillary variables such as BA, the number of burned fragments, ecosystem type, land cover, and burned biomass. The first method studies the zone effect using bootstrapping of Riemannian, full Procrustes, and partial Procrustes distances. The second method explores the validation by using distance permutation tests under uncertainty. The results refer to Fire CCI 5.0 with the best BA description, followed by MCD64C6, MCD64C5.1, MCD45, and Fire CCI 4.1. It was also found that biomass, total BA, and the number of fragments affect the BA product accuracy.