The use of sets of spatiotemporal cortical potential distributions (CPDs) as the basis for cognitive information processing results in a very large space of cognitive elements with natural metrics. Results obtained from current source density (CSD) analysis suggest that in the CPD picture, action potentials may make only a relatively minor contribution to the brain's code. In order to establish if two CPDs are close, we consider standard metrics in spaces of continuous functions, and these may be employed to ascertain if two stimuli will be identified as the same. The correspondence between the electrical activity within brain regions, including not only action potentials but all postsynaptic potentials (PSPs), and CPDs is considered. We examine the possibility of using the CSD approach to find potential distributions using the descriptive approach in which precise sets of times are ascribed to the occurrence of action potentials and PSPs. Using metrics in the multidimensional space of paths of collections of point processes, we show that closeness of CPDs is implied by closeness of sets of spike times and PSP times if a certain metric is used but not others. We also set forth a dynamical model consisting of a system of reaction-diffusion equations for ionic concentrations coupled with nerve membrane potential equations and active transport systems. Making the approximation of a descriptive approach, the correspondence between sets of spike times and PSP times and CPDs is obtained as with the CSD method. However, since it is not possible to ascribe precise times to the occurrence of PSPs and action potentials, the descriptive approach cannot be used to describe the configuration of electrical activity in cortical regions accurately. We also discuss how the CPD framework relates to the binding problem and submillisecond timing.

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