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The COVID-19 disease has forced countries to make a considerable collaborative effort between scientists and governments to provide indicators to suitable follow-up the pandemic's consequences. Mathematical modeling plays a crucial role in quantifying indicators describing diverse aspects of the pandemic. Consequently, this work aims to develop a clear, efficient, and reproducible methodology for parameter optimization, whose implementation is illustrated using data from three representative regions from Chile and a suitable generalized SIR model together with a fitted positivity rate. Our results reproduce the general trend of the infected's curve, distinguishing the reported and real cases. Finally, our methodology is robust, and it allows us to forecast a second outbreak of COVID-19 and the infection fatality rate of COVID-19 qualitatively according to the reported dead cases., Comment: 23 pages, 7 figures

The stability of higher-order time derivative theories using the polymer extension of quantum mechanics is studied. First, we focus on the well-known Pais-Uhlenbeck model and by casting the theory into the sum of two decoupled The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation, called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories; rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrodinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below., Comment: 13 pages, 2 figures

This study aims to understand Chilean parents' and adolescents' conceptions of autonomy and whether they hold different expectations for autonomous behaviors by generation and socioeconomic level. A qualitative approach to data collection was used through separate focus groups of parents and adolescents from different socioeconomic condition. Substantial similarities in parents' and adolescents' conceptions of autonomy were found. Both generations conceive autonomy as multidimensional (i.e., self-sufficiency, decision making, and acting responsibly) and as an age-graded process that is achieved in interaction with parents. Participants emphasize the affective quality of the parent--adolescent relationship, particularly trust, for healthy autonomy achievement. Differences by socioeconomic status (SES) were also apparent in that low-middle-SES parents emphasize the self-sufficiency and responsibility component of autonomy, and adolescents grant more authority to parents in regulating adolescents' behavior compared with their high-middle-SES counterparts.