The Functional Intricacy of Neural Networks A Mathematical Study

Abstract

The motive of the essay is to provide awareness of the functional complexity of our lifestructure and to emphasize the incomprehensibility of this polymorphic mightiness. The consideration is based on the assumption that neurons with axons, dendrites, and synapses form closed functional loops and that axons spread via multiple dendrits and synapses to other neurons, forming in this way highly entangled, constantly operating networks. Two different generalized patterns of neural structures are investigated. The generalization is needed for the purpose of mathematical formulization. In one form of interaction each axon spreads to all other neurons; in the second form there are two bilateral paths of interaction between individual neuron-loops. In both cases a mathematical formula allows to illustrate the doubtless limit of perception of functional comportment of networks, although the investigation hereinconsiders only the architectural structure. With an illustrated examples it is referred to the similarity of the structure of the brain of mammals and the structure of the information networks of technical multi-controlled installations. Thus, it might seem that the basic structure of handling information is universal in nature.