Memory as a Topological Structure on a Surface Network

A special charged surface network with surface spin half particles on it, that can be arranged in topologically inequivalent ways, is introduced. It is shown that action potential-like signals can be generated in the network in response to local surface deformations of a particular kind. Signals generated in this way carry details of the deformation that create them as a form of plasticity that influences the pathways they traverse leaving a topologically stable helical array of spins: a potential memory substrate. The structure is a non transient alignment of surface spins in response to the transient magnetic field generated by the moving charges present in the action potential-like voltage signals generated since particles with spin have magnetic properties. The structure has a natural excitation frequency that may play a role in memory retrieval. Signal generation and memory storage are proposed to depend on the existence of a surface spin structure. We show that such a surface network can capture the intricate topological features of any connectome in the brain. In addition biophysical properties of such a network are examined in order to constrain predictions of how it may function. Highlights Global method for generating one dimensional non-dissipative voltage signal pulses, analytic expressions for them with numerical examples, memory substrate creation, memory lifetimes, surface distortion waves.