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

  • F. T. Arecchi
  • A. Farini
  • N. Megna
Regular Article


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.


Front Face Necker Cube Random Switch Continuous Presentation Binary Correlation 
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Supplementary material

13360_2016_1036_MOESM1_ESM.pdf (59 kb)
Supplementary material


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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Istituto Nazionale di Ottica del CNRFirenzeItaly
  2. 2.Università di FirenzeFirenzeItaly

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