Neuronal topology as set of braids: Information processing, transformation and dynamics

Abstract

Spatial characteristics of brain matter affect dynamics of informational flow. It seems important to investigate into the topology of neural information to better understand biological neural nets as well as for their computer science analogs. Mathematical braids are proposed as tool for modeling the neuronal topology. Neurological basis of neuronal path is reviewed. We demonstrate mathematical algorithms for path description and transformation. A simulation environment for neural braid construction and transformation is implemented. Experimental evaluation of 1310719 braid-defined neural topologies illustrates how neural path intersections affect information processing and memory recall. The mathematical representation of synaptic pruning is proposed. Pruning of neural nets shows the applicability of the approach to the simplification of neural graphs for computational resource saving.