The informational entropy endowed in cortical oscillations

Abstract

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.

Comparative analysis of information measures of the Dirichlet and Neumann two‐dimensional quantum dots

“…Properties of the Rényi and Tsallis entropies are thoroughly addressed in many sources, see, e.g., Refs. [56][57][58] and literature cited therein. Both of them are under very intensive scrutiny with immense applications in extremely diverse branches of the human activity, including their analysis for the dD (with d ≥ 3) quantum structures [10,14,16,18,22-24, 36,59-63].…”

Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials

“…These entropic measures quantify many spreading facets of the quantum probability density all over the hyperspace, which encompass the intrinsic disorder and the geometrical profile of the quantum system. As measures of disorder/uncertainty, the Rényi entropies (which have very important physico-mathematical properties per se [ 31 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]) allow for a much wider quantitative range of applicability than Heisenberg’s measures. This permits, for example, an entropic formulation [ 46 , 47 ] for the uncertainty principle of quantum physics which is stronger [ 42 , 48 ] than the variance-based Heisenberg mathematical formulation [ 49 ] and its generalizations, the radial expectation values [ 50 ].…”

Rényi and Tsallis entropies: three analytic examples

“….. Returning to the applications of the entropies, let us mention that, besides physics and information theory, Rényi measure was used in the investigation of spatial distribution of earthquake epicentres [46], for the analysis of the landscape diversity and integrity [47][48][49][50], the examination of the behaviour of the stock markets [51,52]; characterization of scalp electroencephalogram records corresponding to secondary generalized tonic-clonic epileptic seizures [53]; study of the biological signals [54], exploration and modification of the brain activity [55]; in digital image analysis [56], etc. In turn, Tsallis entropies are widely employed in non-extensive systems, which include the structures and processes characterized by non-ergodicity, long-range correlations and spacetime (multi)fractal geometry; see, e.g., reference [57] for more details.…”