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

In this paper we show how both action potential-like soliton pulses and EEG-like waveform surface excitations can be generated by exploiting the topological connectivity properties of a hypothetical brain connectome, in a surface network, which we prove, exactly captures the topological architecture of any hypothetical brain connectome. This network, it is shown, can generate a wide variety of one dimensional action potential like soliton voltage pulses and soliton generation co-produce two dimension surface waveforms provided the network is charged and has surface spin half particles on it. Both soliton pulses and the co-produced surface waveforms are generated in the network in responds to local pinch surface deformations input signals, that produce signals exploiting the system’s topology. The analytic expressions and oscillation frequencies of the surface waveforms are determined. It is found that the frequencies are inversely relate to amplitudes and that the surface waveforms correspond to the symmetric tiling of a spherical surface. Greens function methods for studying how the waveforms are modulated by other signals are established and are used to explain a complex sequence of surface excitations observed in deep sleep. In an earlier paper it was shown that the charged soliton pulses carry details of the input deformation parameters that create them and transfer this information to the pathways they traverse, as a helical nontransient topologically stable magnetic alignment of surface spins: a memory substrate, with a natural, theoretically determined, excitation frequency range. It is shown how sleep spindles observed in deep sleep, may reflect the presence of these memory excitation frequencies and that soliton pulses and surface waveforms might cooperate to retrieve memory, identify incoming signals and help focus attention.