Mathematical approach to integrating the “neuron-module” and the “cell-assembly”

Abstract

The structural and functional unit of neuropsychic activity is approached in a mathematical way referring to some basic features of both the “neuron-module” and the “cell-assembly.” The proposed units, called modules, have specific synchronous inputs and outputs, more abundant inner than outer connectivity, and their states are assumed representing concepts. Neurons in the model possess finite, discrete scales of states with inhomogeneous distances. Neighbouring relations are asymmetric (like the synapses) and of both intra- and inter-modular type. The actual states of neighbouring cells form a collective state. This is an emergent phenomenon, formally a complex, not necessarily explicit function of the cellular variables. Collective states belonging to the neurons in a module form the modular state. Thus, the influence of different cells on the modular state depends on their arborization, reflecting that the organization of the module holds greater significance than its size. Some of the modular states are assumed as “known”, others are described by fuzzy sets representing definite and ambiguous concepts, respectively. A specified version of the model with application to visual pattern recognition is summarized for illustration.