Characterization of Homicides in Mexico: Analysis of 2015-2022.

BACKGROUND: In Mexico, homicides are the leading cause of death among men aged 15 to 44 years; however, despite their increase in recent decades, the study of this issue is insufficient, given its magnitude and impact. Therefore, this study aimed to characterize the spatial and temporal patterns and associated factors of homicides in Mexico from 2015 to 2022. METHODS: An analytical cross-sectional study was conducted, analyzing death records from the National Institute of Statistics and Geography's general mortality databases. Simple frequencies and incidence rates per 100,000 inhabitants by sex, year, and state of the Mexican Republic were calculated. Mortality was evaluated by age groups and geographic areas, and bivariate logistic regression models with sociodemographic variables were performed. RESULTS: Records of 229,182 homicides in Mexico were analyzed, with a median age of 33 years, interquartile range 18. A total of 203,898 (88.96%) were men and 25,284 (11.04%) were women. The majority of deaths occurred in public places and were caused by firearms; women had a higher percentage of homicides at home. States with high incidence rates for both sexes were Chihuahua, Zacatecas, Michoacán, Colima, and Estado de México. The total years of life lost were 9.19 million years. The national incidence of homicides in men showed an upward trend from 2015 to 2019; however, in the case of women, this incidence increased in various age groups during the study period. Occupation, education, marital status, and place of occurrence had significant associations in the logistic regression models. CONCLUSIONS: This study provides a spatial-temporal characterization of homicides in Mexico between 2015 and 2022, highlighting the high incidence in men and the upward trend in certain age groups among women. These findings underscore the need for preventive measures and public policies to address this issue in a multisectoral manner.

Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes.

We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell-Boltzmann, Fermi-Dirac, or Bose-Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be identified with the system's entropy and analyze the relaxation processes of out-of-equilibrium systems.

Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients.

In this paper, we propose a new algorithm to reconstruct optics surfaces (aka wavefronts) from gradients, defined on a circular domain, by means of the Spherical Harmonics. The experimental results indicate that this algorithm renders the same accuracy, compared to the reconstruction based on classical Zernike polynomials, using a smaller number of polynomial terms, which potentially speeds up the wavefront reconstruction. Additionally, we provide an open-source C++ library, released under the terms of the GNU General Public License version 2 (GPLv2), wherein several polynomial sets are coded. Therefore, this library constitutes a robust software alternative for wavefront reconstruction in a high energy laser field, optical surface reconstruction, and, more generally, in surface reconstruction from gradients. The library is a candidate for being integrated in control systems for optical devices, or similarly to be used in ad hoc simulations. Moreover, it has been developed with flexibility in mind, and, as such, the implementation includes the following features: (i) a mock-up generator of various incident wavefronts, intended to simulate the wavefronts commonly encountered in the field of high-energy lasers production; (ii) runtime selection of the library in charge of performing the algebraic computations; (iii) a profiling mechanism to measure and compare the performance of different steps of the algorithms and/or third-party linear algebra libraries. Finally, the library can be easily extended to include additional dependencies, such as porting the algebraic operations to specific architectures, in order to exploit hardware acceleration features.