Statistical mechanics of neocortical interactions: Nonlinear columnar electroencephalography

ABSTRACT: Columnar firings of neocortex, modeled by a statistical mechanics of neocortical interactions (SMNI), are investigated for conditions of oscillatory processing at frequencies consistent with observed electroencephalography (EEG). A strong inference is drawn that physiological states of columnar activity receptive to selective attention support oscillatory processing in observed frequency ranges. Direct calculations of the Euler-Lagrange (EL) equations which are derived from functional variation of the SMNI probability distribution, giving most likely states of the system, are performed for three prototypical Cases, dominate excitatory columnar firings, dominate inhibitory columnar firings, and in-between balanced columnar firings, with and without a Centering mechanism (CM) (based on observed changes in stochastic background of presynaptic interactions) which pulls more stable states into the physical firings ranges. Only states with the CM exhibit robust support for these oscillatory states. These calculations are repeated for the visual neocortex, which has twice as many neurons/minicolumn as other neocortical regions. These calculations argue that robust columnar support for common EEG activity requires the same columnar presynaptic parameter necessary for ideal short-term memory (STM). It is demonstrated at this columnar scale, that both shifts in local columnar presynaptic background as well as local or global regional oscillatory interactions can effect or be affected by attractors that have detailed experimental support to be considered states of STM. Including the CM with other proposed mechanisms for columnar-glial interactions and for glial-presynaptic background interactions, a path for future investigations is outlined to test for quantum interactions, enhanced by magnetic fields from columnar EEG, that directly support cerebral STM and computation by controlling presynaptic noise. This interplay can provide mechanisms for information processing and computation in mammalian neocortex.