The entanglement entropy of typical pure states and replica wormholes

In a 1+1 dimensional QFT on a circle, we consider the von Neumann entanglement entropy of an interval for typical pure states. As a function of the interval size, we expect a Page curve in the entropy. We employ a specific ensemble average of pure states, and show how to write the ensemble-averaged Rényi entropy as a path integral on a singular replicated geometry. Assuming that the QFT is a conformal field theory with a gravitational dual, we then use the holographic dictionary to obtain the Page curve. For short intervals the thermal saddle is dominant. For large intervals (larger than half of the circle size), the dominant saddle connects the replicas in a non-trivial way using the singular boundary geometry. The result extends the ‘island conjecture’ to a non-evaporating setting.

Traffic flow behavior at a single lane traffic circle

In this paper, we propose a stochastic cellular automata (CA) model to study traffic dynamic at a single-lane traffic circle of [Formula: see text] entry/exit points. The boundaries are controlled by the injecting rates [Formula: see text], [Formula: see text] and the extracting rate [Formula: see text]. Both the cases with and without the splitter islands of width [Formula: see text] are considered. The phase diagrams in the space [Formula: see text] are constructed and the density profiles are also investigated. The variation of the phase diagram with the traffic circle size [Formula: see text], the number of entry point [Formula: see text], and the time needed for drivers to change their exit willingly [Formula: see text] is studied. The results show that the phase diagram in both cases consists essentially of three phases namely free flow, congestion and gridlock. However, the large sized traffic circle shows better performance in the free flow phase, in contrary, the increase of [Formula: see text] enlarges the congestion and the gridlock phases. We have also found that the decrease of [Formula: see text] enhances the traffic flow situation in the traffic circle. Furthermore, as the [Formula: see text] increases, the free flow phase enlarges while the congestion and gridlock ones shrink.

A horse's eye view: size and shape discrimination compared with other mammals

Mammals have adapted to a variety of natural environments from underwater to aerial and these different adaptations have affected their specific perceptive and cognitive abilities. This study used a computer-controlled touchscreen system to examine the visual discrimination abilities of horses, particularly regarding size and shape, and compared the results with those from chimpanzee, human and dolphin studies. Horses were able to discriminate a difference of 14% in circle size but showed worse discrimination thresholds than chimpanzees and humans; these differences cannot be explained by visual acuity. Furthermore, the present findings indicate that all species use length cues rather than area cues to discriminate size. In terms of shape discrimination, horses exhibited perceptual similarities among shapes with curvatures, vertical/horizontal lines and diagonal lines, and the relative contributions of each feature to perceptual similarity in horses differed from those for chimpanzees, humans and dolphins. Horses pay more attention to local components than to global shapes.

Depth Cues Changes Circle Size Judgment Measured by Psychophysical Scaling

The aim of our study was to investigate whether different circle sizes, in conditions of pure size judgment and in a simple contextual judgment with an interfering depth suggesting background, produce different size perceptions. We used the magnitude estimation to obtain the apparent size of circles under two different experimental conditions: with a neutral black background and with a convergent gradient to generate an artificial horizon to evoke depth cues. Twenty-two subjects with normal or corrected-to-normal visual acuity (mean age = 21.3 yrs; SD = 1.6) were tested. The procedure consisted of two gray circles at luminance of 40 cd/m2, separated 10 degrees of visual angle apart from each other. On the left side was always present the reference circle (visual angle of 1.1 degree) in which was assigned an arbitrary value of 50 was assigned. The subjects' task was to judge the size of the circles appearing in the right side of the monitor screen assigning a number proportional to the perceived altered size, relative to the reference circle. Seven different sizes (0.6, 0.8, 1.0, 1.1, 1.3, 1.4, 1.5 degrees) were presented in each condition. Our results have shown a high correlation for circle size and depth conditions (R = 0.987 and R = 0.997) between the logs of the stimuli and the subjective magnitude estimated values. The exponents obtained by the Power Law were 0.79 and 1.09, respectively to each condition. Additionally, a gender effect was observed in which males had showed an expansive perception of size with no dependence on the background. We concluded that in the induced depth condition, the perception of the circle sizes were judged subjectively closer to their respective physical size than in the condition of free visual cues. Our data reinforces the integrative manner of perceptual system when working with the sensory information