Search for: All records

Abstract We prove that if two topologically free and entropy regular actions of countable sofic groups on compact metrizable spaces are continuously orbit equivalent, and each group either (i) contains a w-normal amenable subgroup which is neither locally finite nor virtually cyclic, or (ii) is a non-locally-finite product of two infinite groups, then the actions have the same sofic topological entropy. This fact is then used to show that if two free uniquely ergodic and entropy regular probability-measure-preserving actions of such groups are boundedly orbit equivalent then the actions have the same sofic measure entropy. Our arguments are based on a relativization of property SC to sofic approximations and yield more general entropy inequalities. 

Thermal perception is important in the experience of touching real objects, and thermal display devices are of growing interest for applications in virtual reality, medicine, and wearable technologies. In this paper, we designed a new thermal display, and investigated the perception of spatially varying thermal stimuli, including the thermal grill illusion. The latter is a perceptual effect in which a burning sensation is elicited in response to touching a surface composed of spatially juxtaposed warm and cool areas. Using a computer controlled thermal display, we present experiments in which we measured temporal correlates of the perception of spatially inhomogeneous stimuli, or thermal grills. We assessed the intensity of responses elicited by thermal grill stimuli with different temperature settings, and measured the response time until the onset of burning sensations. We found that thermal grills elicited highly stereotyped responses. The experimental results also indicated that as the temperature difference increases, the intensity increases monotonically, while the response time decreases monotonically. Consequently, perceived intensity was inversely correlated with response time. Under current physiological explanations, responses to thermal stimuli depend on tissue heating, neural processing, and the spatial distribution (or juxtaposition) of surface temperatures. The results of this study could help to inform models accounting for these factors, enabling new applications of the thermal grill illusion.