There is some complementarity of models for the origin of the electroencephalogram (EEG) and neural network models for information storage in brainlike systems. From the EEG models of Freeman, of Nunez, and of the authors' group we argue that the wavelike processes revealed in the EEG exhibit linear and near-equilibrium dynamics at macroscopic scale, despite extremely nonlinear – probably chaotic – dynamics at microscopic scale. Simulations of cortical neuronal interactions at global and microscopic scales are then presented. The simulations depend (...) on anatomical and physiological estimates of synaptic densities, coupling symmetries, synaptic gain, dendritic time constants, and axonal delays. It is shown that the frequency content, wave velocities, frequency/wavenumber spectra and response to cortical activation of the electrocorticogram (ECoG) can be reproduced by a “lumped” simulation treating small cortical areas as single-function units. The corresponding cellular neural network simulation has properties that include those of attractor neural networks proposed by Amit and by Parisi. Within the simulations at both scales, sharp transitions occur between low and high cell firing rates. These transitions may form a basis for neural interactions across scale. To maintain overall cortical dynamics in the normal low firing-rate range, interactions between the cortex and the subcortical systems are required to prevent runaway global excitation. Thus, the interaction of cortex and subcortex via corticostriatal and related pathways may partly regulate global dynamics by a principle analogous to adiabatic control of artificial neural networks. (shrink)

The development of theories of global cortical dynamics, using linear wave theory, owes much to the pioneering work of Nunez. His work leads to clear predictions on relations of brain size, axonal conduction velocity, and the frequencies of the cerebral rhythms. These predictions do not appear to be fulfilled, but their falsification constrains the range of parameters applicable in further formulations.

Freeman's pioneering work -- and neurodynamics in general -- has largely ignored specification of an anatomical framework within which features of coherent objects are represented, associated, deleted, and manipulated in computations. Recent theoretical work suggests such a framework can emerge during embryogenesis by selection of neuron ensembles and synaptic connections that maximize the magnitude of synchrony while approaching ultra-small-world connectivity. The emergent structures correspond to those of both columnar and non-columnar cortex. With initial connections thus organized, spatio-temporal information in sensory (...) inputs can generate systematic and specific patterns of synchronous oscillation, with consequent synaptic storage. The theoretical assemblies of connections resemble experimentally observed 'lego sets', while facilitation and interference among synchronous patterns, particularly when executed by fast synapses under metabolic entanglement, imply powerful parallel computation. (shrink)

Amit's Hebbian model risks being overexplanatory, since it does not depend on specific physiological modelling of cortical ANNs, but concentrates on those phenomena which are modelled by a large class of ANNs. While offering a strong demonstration of the presence of Hebb's “cell assemblies,” it does not offer an equal account of Hebb's “phase sequence” concept.

We outline fresh findings that show that our macroscopic electrocorticographic (ECoG) simulations can account for synchronous multiunit pulse oscillations at separate, simultaneously activated cortical sites and the associated gamma-band ECoG activity. We clarify our views on the approximations of dynamic class applicable to neural events at macroscopic and microscopic scales, and the analogies drawn to classes of ANN behaviour. We accept the need to introduce memory processes and detailed anatomical and physiological information into any future developments of our simulations. On (...) the issue of intrinsic cortical stability and the role of extrinsic fibre systems in maintaining stability, we argue that this position is not in extreme contradiction to those of our commentators, and that the mechanisms implicit in our simulations' properties imply rich computational possibilities. We discuss some of the reasons for and against the existence of significant global resonances in the brain and explain why such behaviour appears absent in our simulations. Last, we discuss other phenomena, such as rhythmic driving of the cortex, which have not yet been introduced into our models, and indicate lines for future development of the simulations. (shrink)