Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

Female hippocampus vulnerability to environmental stress, a precipitating factor in tau aggregation pathology

Tau-mediated neurodegeneration is a central event in Alzheimer's disease (AD) and other tauopathies. Consistent with suggestions that lifetime stress may be a clinically-relevant precipitant of AD pathology, we previously showed that stress triggers tau hyperphosphorylation and accumulation; however, little is known about the etiopathogenic interaction of chronic stress with other AD risk factors, such as sex and aging. This study focused on how these various factors converge on the cellular mechanisms underlying tau aggregation in the hippocampus of chronically stressed male and female (middle-aged and old) mice expressing the most commonly found disease-associated Tau mutation in humans, P301L-Tau. We report that environmental stress triggers memory impairments in female, but not male, P301L-Tau transgenic mice. Furthermore, stress elevates levels of caspase-3-truncated tau and insoluble tau aggregates exclusively in the female hippocampus while it also alters the expression of the molecular chaperones Hsp90, Hsp70, and Hsp105, thus favoring accumulation of tau aggregates. Our findings provide new insights into the molecular mechanisms through which clinically-relevant precipitating factors contribute to the pathophysiology of AD. Our data point to the exquisite sensitivity of the female hippocampus to stress-triggered tau pathology.

Preschool education in Brazil: does public supply crowd out private enrollment?

Expanding access to preschool education is a particularly important policy issue in developing countries, where enrollment rates are generally much lower, and where private institutions constitute a much larger share of the formal preschool sector, than in developed countries. This paper examines if an expansion in the supply of public preschool crowds-out private enrollment using rich data for municipalities in Brazil from 2000 to 2006, where federal transfers to local governments change discontinuously with given population thresholds. Results from a regression-discontinuity design reveal that larger federal transfers lead to a significant expansion of local public preschool services, but show no evidence of crowding-out of private enrollment, nor of negative impacts on the quality of private providers. This finding is consistent with a theory in which households differ in willingness-to-pay for preschool services, and private suppliers optimally adjust prices in response to an expansion of lower-quality, free-of-charge public supply. In the context of the model, the absence of crowding-out effects of more public preschool providers can be rationalized by the existence of relatively large differences in willingness-to-pay for preschool services across different demand segments. Our theoretical and empirical findings therefore suggest that in developing country settings characterized by relatively high income inequality, an expansion in public preschool supply will likely significantly increase enrollment among the poorest segments of society, and need not have adverse effects on the quantity or quality of local private supply.