A topological method of generating action potentials and EEG oscillations in a surface network

Abstract

The brain is a source of continuous electrical activity, which include one dimensional voltage pulses (action potentials) that propagate along nerve fibres, transient localised oscillations, and persistent surface oscillations in five distinct frequency bands. However, a unified theoretical framework for modelling these excitations is lacking. In this paper we provide such a framework by constructing a special surface network in which all observed brain-like signals, including surface oscillations, can be generated by topological means. Analytic expressions for all these excitations are found and the values of the five frequency bands of surface oscillations are correctly predicted. It is shown how input signals of the system produce their own communication code to encode the information they carry and how the response output propagating signals produced carry this input information with them and can transfer it to the pathways they traverse as a non-transient topological memory structure of aligned spin-half protons. It is conjectured that the memory structure is located in the insulating sheaths of nerve fibres and are stable only if the pathways between assembly of neurons, that represents a memory structure, includes loops. The creation time and size of memory structures is estimated and a memory specific excitation frequencies for a memory structure is identified and determined, which can be used to recall memories.