RESUMEN
On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify the rate of convergence to this profile uniformly in relative error, showing the rate is either exponentially fast (with a rate constant predicted by the spectral gap), or algebraically slow (which is only possible in the presence of non-integrable zero modes). In the first case, the nonlinear dynamics are well-approximated by exponentially decaying eigenmodes up to at least twice the gap; this refines and confirms a 1980 conjecture of Berryman and Holland. We also improve on a result of Bonforte and Figalli by providing a new and simpler approach which is able to accommodate the presence of zero modes, such as those that occur when the vanishing profile fails to be isolated (and possibly belongs to a continuum of such profiles).
RESUMEN
Since the outbreak of the COVID-19 pandemic in December 2019 and the associated restrictions, mental health in children and adolescents has been increasingly discussed in the media. Negative impacts of the pandemic, including a sharp increase in psychopathology and, consequently, reduced quality of life, appear to have particularly affected children and young people, who may be especially vulnerable to the adverse effects of isolation. Nevertheless, many children and adolescents have managed to cope well with the restrictions, without deterioration of their mental health. The present study therefore explored the links between COVID-19 infection (in oneself or a family member, as well as the death of a family member due to the virus), protective factors such as self-efficacy, resilience, self-esteem, and health-related quality of life, and measures of psychopathology such as depression scores, internalizing/externalizing problems, emotion dysregulation, and victimization. For this purpose, we examined data from 2129 adolescents (mean age = 12.31, SD = 0.67; 51% male; 6% born outside of Germany) using a structural equation model. We found medium to high loadings of the manifest variables with the latent variables (COVID-19, protective factors, and psychopathology). Protective factors showed a significant negative correlation with psychopathology. However, COVID-19 had a weak connection with psychopathology in our sample. External pandemic-related factors (e.g., restrictions) and their interaction with existing psychopathology or individual protective factors appear to have a greater influence on young people's mental health than the impact of the virus per se. Sociopolitical efforts should be undertaken to foster prevention and promote individual resilience, especially in adolescence.
Asunto(s)
COVID-19 , Trastornos Mentales , Niño , Humanos , Masculino , Adolescente , Femenino , Trastornos Mentales/epidemiología , Trastornos Mentales/psicología , Factores Protectores , Pandemias , Calidad de Vida , COVID-19/epidemiologíaRESUMEN
We study the evolution of solutions to the two-dimensional Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the vorticity is merely [Formula: see text] integrable for some [Formula: see text], we show that the evolving vortex regions remain concentrated around points, and these points are close to solutions to the Helmholtz-Kirchhoff point vortex system. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
RESUMEN
Humans often show reduced social attention in real situations, a finding rarely replicated in controlled laboratory studies. Virtual reality is supposed to allow for ecologically valid and at the same time highly controlled experiments. This study aimed to provide initial insights into the reliability and validity of using spherical videos viewed via a head-mounted display (HMD) to assess social attention. We chose five public places in the city of Würzburg and measured eye movements of 44 participants for 30 s at each location twice: Once in a real environment with mobile eye-tracking glasses and once in a virtual environment playing a spherical video of the location in an HMD with an integrated eye tracker. As hypothesized, participants demonstrated reduced social attention with less exploration of passengers in the real environment as compared to the virtual one. This is in line with earlier studies showing social avoidance in interactive situations. Furthermore, we only observed consistent gaze proportions on passengers across locations in virtual environments. These findings highlight that the potential for social interactions and an adherence to social norms are essential modulators of viewing behavior in social situations and cannot be easily simulated in laboratory contexts. However, spherical videos might be helpful for supplementing the range of methods in social cognition research and other fields. Data and analysis scripts are available at https://osf.io/hktdu/ .