Multidimensional general convexity for stochastic processes and associated with Hermite-Hadamard type integral inequalities

In this study, we idetified multidimensional general convex stochastic processes. Concordantly, we obtained some important results related stochastic processes. Moreover, we derived some Hermite-Hadamard type integral inequalities for these stochastic processes.

Six-Month-Old Infants' Perception of the Hollow Face Illusion: Evidence for a General Convexity Bias

Corrow, Granrud, Mathison, and Yonas (2011, Perception, 40, 1376–1383) found evidence that 6-month-old infants perceive the hollow face illusion. In the present study we asked whether 6-month-old infants perceive illusory depth reversal for a nonface object and whether infants' perception of the hollow face illusion is affected by mask orientation inversion. In experiment 1 infants viewed a concave bowl, and their reaches were recorded under monocular and binocular viewing conditions. Infants reached to the bowl as if it were convex significantly more often in the monocular than in the binocular viewing condition. These results suggest that infants perceive illusory depth reversal with a nonface stimulus and that the infant visual system has a bias to perceive objects as convex. Infants in experiment 2 viewed a concave face-like mask in upright and inverted orientations. Infants reached to the display as if it were convex more in the monocular than in the binocular condition; however, mask orientation had no effect on reaching. Previous findings that adults' perception of the hollow face illusion is affected by mask orientation inversion have been interpreted as evidence of stored-knowledge influences on perception. However, we found no evidence of such influences in infants, suggesting that their perception of this illusion may not be affected by stored knowledge, and that perceived depth reversal is not face-specific in infants.