Francisco Luis Cumbrera

Spinel oxides of formula AB2O4 exhibit a wide range of cation distributions between tetrahedral and octahedral sites. In this study, a vacancy-explicit thermodynamic model is developed that incorporates configurational entropy, ligand-field stabilisation, and non-ideal cation interactions parameterised through a quadratic Redlich–Kister term, aimed at describing inversion equilibria in both ideal and defect-rich spinels where classical vacancy-free models may fail. The formulation is expressed in reduced form (i.e., normalised by “RT”) and reduces the thermodynamic description to two state variables: the inversion parameter ([[EQUATION]]) and the vacancy fraction ([[EQUATION]]). Application to representative spinels shows contrasting behaviours. For MgAl2O4 and Co3O4 (which is Co2+(Co3+)2O4) the equilibrium inversion is reproduced without invoking measurable vacancy populations, consistent with experimental observations. In contrast, Fe3O4 (which is Fe3+(Fe2+Fe3+)O4) and NiFe2O4 require a finite vacancy contribution, with an estimated vacancy formation energy of about 1.2 eV per defect. The analysis further identifies conditions under which the free-energy function g([[EQUATION]],[[EQUATION]]) becomes non-convex, leading to bistability and metastable states between low- and high-inversion configurations. These results demonstrate that an explicit thermodynamic treatment of vacancies is essential for describing both equilibrium inversion and possible multi-stability in defective or non-stoichiometric spinels.

The genetic code is commonly described as a redundant mapping from nucleotide triplets to amino acids, but this redundancy does not make all nucleotide substitutions equivalent. A physical mutation rate at the DNA level may translate into silent changes, conservative amino-acid substitutions, severe missense events, or nonsense mutations. Here, we develop a communication-theoretic framework to quantify how nucleotide-level errors are transformed into semantic degradation of protein-coding information. Single-nucleotide substitutions were modelled as an error channel with variable transition/transversion structure, and their effects were weighted using a normalized physicochemical distance between amino acids, with nonsense mutations assigned maximal cost. This allowed the definition of codon-level semantic cost, sequence-level degradation, and synonymous-codon protection scores.The framework first confirmed that the standard genetic code reduces expected semantic cost relative to randomized genetic-code baselines. At fixed nucleotide substitution probability, semantic degradation depended strongly on the transition/transversion spectrum, showing that physical error rate and genetic-information degradation are not equivalent quantities. The model was then applied to real coding sequences from the RefSeq Escherichia coli K-12 MG1655 assembly. Gene-level analysis revealed substantial heterogeneity in semantic vulnerability across CDS, driven by codon composition, synonymous-codon choice, nonsense susceptibility, and sequence length.Protein-preserving synonymous null models were used to separate amino-acid-composition effects from codon-choice effects. Relative to uniformly chosen synonymous alternatives, real E. coli CDS showed lower semantic substitution cost, increased silent-error protection, and reduced nonsense vulnerability. Much of this signal was explained by genome-wide codon-usage bias, but a subset of genes remained locally protected or locally vulnerable after controlling for global codon usage. Importantly, high-confidence essential genes were enriched among locally protected CDS and depleted among locally vulnerable CDS. This association remained robust across essentiality definitions, mutation-channel assumptions, multivariate controls, and random-label permutation tests.These results support a layered view of genetic-information robustness: the standard genetic code provides a primary semantic-protection layer, organism-wide codon usage provides a secondary modulation, and gene-specific synonymous choice introduces local heterogeneity associated with functional constraint. The proposed framework links mutation-channel parameters to interpretable measures of semantic degradation and provides a quantitative bridge between molecular error processes, codon usage, and gene essentiality.

Machine learning‐based algorithms have been widely applied recently in different areas due to its ability to solve problems in all fields. In this research, machine learning techniques classifying the Bravais lattices from a conventional X‐ray diffraction diagram have been applied. Indexing algorithms are an essential tool of the preliminary protocol for the structural determination problem in crystallography. The task of reverting the obtained information in reciprocal lattice to direct space is a complex issue. As an alternative way to afford this problem, different machine learning algorithms have been applied and a comparison between them has been conducted. The obtained accuracy was 95.9% using 10‐fold cross‐validation (while the best result obtained so far has been 84%). A model based on Bragg positions was our unique predictor, allowing us to obtain the set of the interplanar lattice distances. Our model was successfully checked with a complex example. In addition, our procedure incorporates the following advantages: robustness versus imprecision in data acquisition and reduction of the amount of necessary input data. This is the first time so far that such classification has been carried out in true ab initio condition.

The superplastic behavior of alumina-based nanostructured ceramics (Al₂O₃) is an important issue in the world of materials. The main body of this paper is an analysis of the creep behavior of polycrystals, with grain boundary sliding as the main deformation mechanism at high temperatures. Concomitant accommodation of grain shapes to preserve spatial continuity has a comparatively small effect on the strain rate. The constitutive equations for small deformations, relating strain and strain rate, derived from two models for grain sliding, are compared with the experimental data with their respective uncertainties. The data follow from experiments on the plastic deformation of alumina composites reinforced, on the one hand by graphene oxide, and on the other hand by carbon nanofibers sintered by SPS. The results show good agreement between experiment and theory for these advanced ceramics, particularly for one of the assumed models. The values obtained of ξ² for model A were in the interval 0.0002–0.1189, and for model B were in the interval 0.000001–0.0561. The values obtained of R² for model A were in the interval 0.9122–0.9994, and for model B were in the interval 0.9586–0.9999. The threshold stress was between (3.05 · 10⁻¹⁵–25.68) MPa.