Abstract
In this paper we complete a project to demonstrates that both action potential like and EEG waveform like brain excitations can be viewed as excitations generated by exploiting the topological connectivity properties of the brain, thereby relating function to form. This is done by first proving that it is possible to find a two dimensional mathematical surface network that exactly captures the topological architecture of any hypothetical brain connectome. It is then suggested that such a surface can be taken to be a mathematical representation of the brain if it is charged and if it has surface spin half particles as then it can be shown that the surface can generate a variety of one dimensional action potential like soliton voltage pulse signals and co-producing two dimension surface EEG like waveforms in responds to local surface pinch deformations input signals. The charged soliton pulses found are shown to carry details of the input signals deformation parameters that create them and can transfer this information to the pathways they traverse as a helical non transient topologically stable alignment of surface spins: a memory substrate. The substrate has a natural, theoretically determined, excitation frequency that can be used to retrieve memories by resonance. In an earlier work soliton pulse generation and memory creation stability issues were discussed. Here we show how EEG like excitations are co-produced and establish their properties. We determine the analytic expressions, of EEG waveforms, determine their frequencies, show that frequencies are inversely relate to the waveform amplitudes, and related to symmetric tiling of a sphere and show how they are modulated by other signals. As an example we describe how the scheme can be used to explain the complex sequence of EEG excitations observed in deep sleep. We speculate on how action potentials and EEG waveforms cooperate to retrieve memory and help to focus attention.
Competing Interest Statement
The authors have declared no competing interest.