A test of multiple correlation temporal window characteristic of non-Markov processes

Abstract

We introduce a sensitive test of memory effects in successive events. The test consists of a combination K of binary correlations at successive times. K decays monotonically from K = 1 for uncorrelated events as a Markov process. For a monotonic memory fading, $ K<1$ always. Here we report evidence of a $ K>1$ temporal window in cognitive tasks consisting of the visual identification of the front face of the Necker cube after a previous presentation of the same. We speculate that memory effects provide a temporal window with $ K>1$ and this experiment could be a possible first step towards a better comprehension of this phenomenon. The $ K>1$ behaviour is maximal at an inter-measurement time $ \tau$ around 2s with inter-subject differences. The $ K>1$ persists over a time window of 1s around $ \tau$ ; outside this window the $K<1$ behaviour is recovered. The universal occurrence of a $ K>1$ window in pairs of successive perceptions suggests that, at variance with single visual stimuli eliciting a suitable response, a pair of stimuli shortly separated in time displays mutual correlations.