Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.Comment: to appear in Quarterly of Applied Mathematic

The actual pressure and temperature at the melt of elemental vanadium

It is claimed that all of the pressure scales of the reported melting curves derived by diamond anvil cell experiments require a correction which takes into account the pressure thermal shift, where vanadium is an illustrative example. The linear behavior of the thermal pressure (Pth) vs. the temperature, as predicted by first principles theoretical assumptions is then experimentally confirmed. This allows extrapolation to determine of the actual pressure and thermal temperature at the melt. Accounting for the role of the pressure transmitting media in diamond anvil cell experiments, the analysis of elemental vanadium melting curve is presented. It is shown that the appropriate correction of shock waves melting data which takes into account the radiation absorbed by the LiF window, applies only to vanadium metal. The correct pressure scale of vanadium metal as derived by diamond anvil cell is presented.Comment: 17 pages, 4 figure

A Baseline for Detecting Out-of-Distribution Examples in Image Captioning

Image captioning research achieved breakthroughs in recent years by developing neural models that can generate diverse and high-quality descriptions for images drawn from the same distribution as training images. However, when facing out-of-distribution (OOD) images, such as corrupted images, or images containing unknown objects, the models fail in generating relevant captions. In this paper, we consider the problem of OOD detection in image captioning. We formulate the problem and suggest an evaluation setup for assessing the model's performance on the task. Then, we analyze and show the effectiveness of the caption's likelihood score at detecting and rejecting OOD images, which implies that the relatedness between the input image and the generated caption is encapsulated within the score.Comment: Accepted to ACM Multimedia (MM) 202

Brain Activity in Valuation Regions While Thinking About the Future Predicts Individual Discount Rates

People vary widely in how much they discount delayed rewards, yet little is known about the sources of these differences. Here we demonstrate that neural activity in ventromedial prefrontal cortex (VMPFC) and ventral striatum (VS) when human subjects are asked to merely think about the future—specifically, to judge the subjective length of future time intervals—predicts delay discounting. High discounters showed lower activity for longer time delays, while low discounters showed the opposite pattern. Our results demonstrate that the correlation between VMPFC and VS activity and discounting occurs even in the absence of choices about future rewards, and does not depend on a person explicitly evaluating future outcomes or judging their self-relevance. This suggests a link between discounting and basic processes involved in thinking about the future, such as temporal perception. Our results also suggest that reducing impatience requires not suppression of VMPFC and VS activity altogether, but rather modulation of how these regions respond to the present versus the future