Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Higher Visual Functions in the Upper and Lower Visual Fields: a pilot study in healthy subjects

Visual perception is not identical in the upper and lower visual hemifields. The mechanisms behind this difference can be found at the retinal, cortical, or higher attentional level. In this study, a new visual test battery, that involves real-time comparisons of complex visual stimuli, such as shape of objects, and speed of moving dot patterns, in the upper and lower visual hemifields, is presented. This study represents, to our knowledge, the first to implement such a visual test battery in an immersive environment composed of a hemisphere, in order to present visual stimuli in precise regions of the visual field. Ten healthy volunteers were tested in this pilot study. The results showed a higher accuracy in the image matching when the visual test was performed in the lower visual hemifield.

The effects of qualitatively different acute physical activity interventions in real-world settings on executive functions in preadolescent children

There is growing evidence indicating a positive effect of acute physical activity on cognitive performance in children. Most of the evidence originates, however, from studies in highly controlled laboratory settings. The aim of the present study was to investigate whether the same effects can be found in more real-world settings. We examined the effects of qualitatively different acute physical activity interventions on the three core dimensions of executive functions (updating, inhibition, shifting). In an experimental between-subject design, 219 ten to twelve year-olds were assigned to one of four conditions which varied systematically in physical activation and cognitive engagement. Executive functions were measured before and immediately after the intervention. Contrary to the hypothesis, no effects of acute physical activity with and without cognitive engagement were found on executive functions in the overall sample. Only children with higher fitness and/or higher academic achievement benefitted from the interventions in terms of their updating performance. Thus, the results indicate that it may be more difficult to attain positive effects through acute physical activity in real-world settings than in laboratory settings and that physiological and cognitive requirements may have to be adjusted to individual capacity to make an intervention effective.