Universidad Autónoma del Estado de Morelos

We present a molecular orbital (MO) localization scheme based on an information-theoretic measure of orbital delocalization. The method minimizes a Shannon-type functional constructed from the squared orbital amplitudes using a quadratic form derived from a Taylor expansion. This leads to a simple and computationally efficient localization criterion that depends only on quartic overlap integrals, thereby avoiding the costly electron repulsion terms required in some conventional approaches. The resulting orbitals exhibit a systematic reduction in entropy relative to canonical MOs while preserving chemically meaningful features such as σ and π character. The method converges rapidly, particularly in ionic systems where the orbitals are already strongly localized, and shows a monotonic decrease of the rotation angles during the Jacobi sweeps, indicating stable numerical behavior.

This study presents an extensive mathematical framework for the stability analysis and validation of advanced control applications in continuous, nonlinear, hybrid, and Caputo–Fabrizio fractional-order systems. The proposed methodology integrates Lyapunov theory, Input-to-State Stability analysis, passivity, and small-gain techniques into a cohesive, generalizable criterion suitable for both linear and nonlinear dynamics. The method covers systems that are defined by Caputo–Fabrizio fractional derivatives and can handle uncertainty, disturbances, and mixed events. Validation is part of the stability analysis, which combines proof-based assurances with verification through simulation in real-world conditions. Scenario-based probabilistic analysis links the results of Monte Carlo tests to formal risk limitations. This makes it possible to verify that stability and contract compliance are both fully assured. Case studies featuring robotic manipulators, process control with model predictive control, and adaptive aeronautical systems demonstrate the methodology, achieving significant robustness margins and statistical performance assurance. This unified technique provides a theoretically robust and empirically substantiated pathway from controller synthesis to implementation.

Electromagnetically forced flows in shallow electrolyte layers offer a versatile and nonintrusive method for exploring quasi-two-dimensional fluid dynamics. This review focuses on the experimental and theoretical aspects of such flows driven by Lorentz forces generated by the interaction of injected electric currents and the applied magnetic fields. The method is applicable to both liquid metals and electrolytes, with the latter more commonly used due to their wide availability and ease of handling. Experimental aspects of the method and key components of mathematical flow analysis are discussed. Initially developed for geophysical flow modeling, the method has been instrumental in exploring various other physical phenomena including vortex and wake dynamics, spatiotemporal chaos, and mixing processes. The review also addresses the challenges of achieving true two-dimensionality in laboratory settings and discusses the influence of various parameters, such as layer thickness and forcing intensity, on the flow behavior. Future research directions in the field are highlighted.

In canonical quantum gravity, time does not appear as a fundamental coordinate, posing the longstanding problem of how dynamical evolution arises in a fundamentally timeless universe. In this work, we propose that entropy—interpreted as a coarse-grained, monotonically increasing measure of system complexity—can serve as an emergent internal clock. We unify three complementary mechanisms underpinning this idea: (i) the monotonic growth of entanglement entropy under unitary dynamics, (ii) thermal modular flow associated with Kubo-Martin-Schwinger states, and (iii) relational time from the Page–Wootters framework. These mechanisms jointly define a physical arrow and parametrization of time grounded in the informational structure of the quantum state. From this foundation, we derive explicit entropic time laws of the form τ (Δ S)=( Δ S/λ) ^1/γ , showing how the parameters (q,N_0,λ ,γ ) emerge from microscopic statistical properties such as non-extensive correlations, phase space growth, and entropy production rates. We apply this framework to cosmological epochs, identifying entropy increase across inflation, radiation and matter domination as a natural proxy for internal time progression. This entropic approach provides a unified view linking quantum foundations, thermodynamic irreversibility, and cosmological evolution. We also discuss interpretational subtleties, clarifying how entropic time differs from coordinate time and under what conditions it defines a meaningful temporal structure. We emphasize that the entropic time, τ , provides an arrow and parametrization of change in relational regimes (Wheeler–DeWitt,Page–Wootters, KMS/modular frameworks), but it is not proposed as a universal bijective substitute for coordinate time, t.

Hypervirulent Klebsiella pneumoniae is a pathotype capable of causing invasive infections with high morbidity and mortality rates. In this study, we conducted a surveillance analysis of hypervirulent isolates circulating in Mexico to characterize their phenotypic and genomic features. Presumptive hypervirulent isolates were identified at a frequency of 6.48 % (19/293), comprising 17 K. pneumoniae sensu stricto and two K. quasipneumoniae subsp. similipneumoniae. Isolates were predominantly recovered from male patients (12/19, 63 %). Clinical samples were obtained from lower respiratory tract (15/19, 78.9 %), blood (3/19, 15.7 %), and pleural fluid (1/19, 5.2 %). Further genetic and phenotypic analyses revealed substantial heterogeneity among these strains, including significant phenotype-genotype discordance. Notably, this cohort includes the first identified convergent hypervirulent K. pneumoniae strain in Mexico, as well as two hypervirulent K. quasipneumoniae isolates, a phenomenon that is less frequent in K.quasipneumoniae than in K. pneumoniae. These discrepancies prompted us to propose a local classification scheme based on the presence of virulence-associated genes, lethality in mice and antimicrobial susceptibility. Phylogenetic and pangenome analysis revealed clustering patterns associated with sequence types and capsule serotypes. The data generated in this study contribute to a deeper understanding of Hypervirulent K. pneumoniae species complex biology and provide valuable insights into the diversity of strains currently circulating in Mexico.