Towards a unified brain theory

Abstract

An approach to collective aspects of the neocortical system is formulated by methods of modern non-equilibrium statistical mechanics. Microscopic neuronal synaptic interactions are first spatially averaged over columnar domains. These spatially ordered domains include well formulated fluctuations that retain contact with the original physical synaptic parameters. They also are a suitable substrate for macroscopic spatial-temporal regions described by Fokker-Planck and Lagrangian formalisms. This development clarifies similarities and differences among previous studies, suggests new analytically supported insights into neocortical function and permits future approximation or elaboration within current paradigms of collective systems.

Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory

“…In nature, complex systems often present different phenomena at different scales. In this context, a plausible model of statistical mechanics of neocortical interactions (SMNI) has been developed over the past decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Some recent experimental work further justifies the SMNI mathematical development of the microscopic scale into mesocolumns [17].…”

Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography

“…Limiting cases of linear macroscopic theories of intracortical interaction predict local wav e phenomena and obtain dispersion relations with typical wav e numbers k= 10 to 100 cm −1 and dominant frequencies in the general range of human spontaneous EEG (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) [17,47]. However, human scalp potentials are spatially filtered by both distance and tissue between cortical current sources and surface electrodes so that scalp EEG power is attenuated to about 1% of its cortical value at k= 1 or 2 cm −1 .…”

Statistical Mechanics of Neocortical Interactions: Portfolio of Physiological Indicators

“…Since 1981, a series of papers on the statistical mechanics of neocortical interactions (SMNI) has been developed to model columns and regions of neocortex, spanning mm to cm of tissue. Most of these papers have dealt explicitly with calculating properties of STM and scalp EEG in order to test the basic formulation of this approach [6,7,9,10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”