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

Abstract

AbstractWe prove that it is possible to construct a mathematical surface network that exactly captures the topological connectivity architecture of any hypothetical brain connectome. The surface has electrons. Local surface deformations are universal input signals of the network. They have signal specific parameters and change the topology of the subunit to that of a sphere, to produce a wide variety of output signals that include one dimensional soliton pulses, transient localized excitations and EEG-like surface waveforms. Thus the two topological numbers of the subunit,gthat reflects its connectivity andWthat reflects topological arrangements of the surface electron spin magnets are reduced to zero, the topological numbers of the sphere. Both of these topological numbers as well as the signal specific deformation parameters are carried away by the soliton pulses. The charged moving soliton transfers the signal specific distortion parameters they carry to create a non-transient helical electron spin-magnet alignment, a memory trace, with a theoretically estimated specific frequency label. The structure is created by the magnetic field generated by the charged moving solitons. A dynamical principle that requires that all input signals and responses to them must respect the mathematical properties of the network surface is used to derive all results. Predictions regarding the the frequencies and shapes of the EEG like waveforms are made that are consistent with observations. A theoretical interpretation of a complex sequence of EEG events observed in deep sleep, where it is assumed that signal blocking events play a key role,is carried out using a Greens function formula derived for calculating the response of EEG waveforms to input signals. Memory retrieval is shown to have quantum computer like features.