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Here we introduce a hierarchical approach to brain dynamics using Freeman K sets, including the hierarchy of \(K0\) , \(KI\) , \(KII\) , and \(KIII\) sets. They correspond to brain scales starting from the sub-mm range to the complete hemisphereHemisphere. The original formulation of Freeman K sets uses a system of ordinary differential equations (ODEs). Random Graph Theory (RGT) is proposed to devise a discrete calculus in which the element is not a neuron but a functional element corresponding to the collective of neurons that participate in time-sharing. RGT-based mathematical formulation is especially useful in interpreting rapid switches in cortical dynamics as phase transitions.

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Hierarchical Neuropercolation Models and Large-Scale Simulations

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  • 发表日期：

    2026年

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  • Robert Kozma,
  • Walter J. Freeman

摘要

Here we introduce a hierarchical approach to brain dynamics using Freeman K sets, including the hierarchy of \(K0\) , \(KI\) , \(KII\) , and \(KIII\) sets. They correspond to brain scales starting from the sub-mm range to the complete hemisphereHemisphere. The original formulation of Freeman K sets uses a system of ordinary differential equations (ODEs). Random Graph Theory (RGT) is proposed to devise a discrete calculus in which the element is not a neuron but a functional element corresponding to the collective of neurons that participate in time-sharing. RGT-based mathematical formulation is especially useful in interpreting rapid switches in cortical dynamics as phase transitions.