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

The brain is a source of continuous electrical activity, which includes one-dimensional voltage pulses (action potentials) that propagate along nerve fibres, transient localized oscillations and persistent surface oscillations in five distinct frequency bands. However, a unified theoretical framework for modelling these excitations is lacking. In this article, 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 is stable only if the pathways between the assembly of neurons, which represents a memory structure, include loops. The creation time and size of memory structures are estimated, and a memory-specific excitation frequency for a memory structure is identified and determined, which can be used to recall memories.