The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Self-motion perception influences number processing: evidence from a parity task

We investigated the role of horizontal body motion on the processing of numbers. We hypothesized that leftward self-motion leads to shifts in spatial attention and therefore facilitates the processing of small numbers, and vice versa, we expected that rightward self-motion facilitates the processing of large numbers. Participants were displaced by means of a motion platform during a parity judgment task. We found a systematic influence of self-motion direction on number processing, suggesting that the processing of numbers is intertwined with the processing of self-motion perception. The results differed from known spatial numerical compatibility effects in that self-motion exerted a differential influence on inner and outer numbers of the given interval. The results highlight the involvement of sensory body motion information in higher-order spatial cognition.

Self-motion perception training: thresholds improve in the light but not in the dark

We investigated perceptual learning in self-motion perception. Blindfolded participants were displaced leftward or rightward by means of a motion platform and asked to indicate the direction of motion. A total of eleven participants underwent 3,360 practice trials, distributed over twelve (Experiment 1) or 6 days (Experiment 2). We found no improvement in motion discrimination in both experiments. These results are surprising since perceptual learning has been demonstrated for visual, auditory, and somatosensory discrimination. Improvements in the same task were found when visual input was provided (Experiment 3). The multisensory nature of vestibular information is discussed as a possible explanation of the absence of perceptual learning in darkness.