Cognitive Neurodynamics

, Volume 12, Issue 5, pp 501–507 | Cite as

The informational entropy endowed in cortical oscillations

  • Arturo TozziEmail author
  • James F. Peters
  • Mehmet Niyazi Çankaya
Research Article


A two-dimensional shadow may encompass more information than its corresponding three-dimensional object. Indeed, if we rotate the object, we achieve a pool of observed shadows from different angulations, gradients, shapes and variable length contours that make it possible for us to increase our available information. Starting from this simple observation, we show how informational entropies might turn out to be useful in the evaluation of scale-free dynamics in the brain. Indeed, brain activity exhibits a scale-free distribution that leads to the variations in the power law exponent typical of different functional neurophysiological states. Here we show that modifications in scaling slope are associated with variations in Rényi entropy, a generalization of Shannon informational entropy. From a three-dimensional object’s perspective, by changing its orientation (standing for the cortical scale-free exponent), we detect different two-dimensional shadows from different perception angles (standing for Rényi entropy in different brain areas). We show how, starting from known values of Rényi entropy (easily detectable in brain fMRIs or EEG traces), it is feasible to calculate the scaling slope in a given moment and in a given brain area. Because changes in scale-free cortical dynamics modify brain activity, this issue points towards novel approaches to mind reading and description of the forces required for transcranial stimulation.


Rényi entropy Power laws Nervous system Scale-free Shadows Central nervous system 



The Authors would like to thank Andrew and Alexander Fingelkurts for commenting upon an earlier version of this manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Computational Intelligence LaboratoryUniversity of ManitobaWinnipegCanada
  2. 2.Department of Electrical and Computer EngineeringUniversity of ManitobaWinnipegCanada
  3. 3.Department of Mathematics, Faculty of Arts and SciencesAdıyaman UniversityAdıyamanTurkey
  4. 4.Applied Sciences School, Department of International Trading, Department of Statistics, Faculty of Arts and ScienceUsak UniversityUsakTurkey

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