Brain electric activity exhibits two important features: oscillations with different timescales, characterized by diverse functional and psychological outcomes, and a temporal power law distribution, which appears as a straight line when plotted on logarithmic scales in a log power versus log frequency plot. In order to investigate the relationships between low- and high- frequency spikes in the brain, we used a variant of the Borsuk-Ulam theorem which states that, when we assess the nervous activity as embedded in a sphere equipped with a fractal dimension, we achieve two antipodal points with similar features (the slow and fast, scale-free oscillations). We demonstrate that slow and fast nervous oscillations are correlated and provide, through the Bloch theorem from solid-state physics, the possible equation which links the two timescale activities.
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[v1] 2016-09-02 12:31:10
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