ON THE PROPERTIES OF RANDOMLY CONNECTED McCULLOCH-PITTS NETWORKS: DIFFERENCES BETWEEN INPUT-CONSTANT AND INPUT-VARIANT NETWORKS

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Abstract
The properties of randomly connected McCulloch-Pitts networks are examined by analytical methods as well as by computer simulation. A classification of the activity transition functions for input-constant networks is provided and a theorem is proved on a necessary and sufficient condition for the symmetry of the activity transition function. The activity transition functions of input-constant networks were compared with those of three types of input variant networks. It is shown that input constant networks are representative for other types of randomly connected networks as long as no more than 50% of the cells are active. Above 50% activation, input constant networks have the most peculiar activity transition function. The time behavior of mean activity in the network was less well predictable in input-variant as compared to input-constant ones. The conditions for the existence of autonomous oscillations are the same for all types of random connectivity. Implications of the findings for the interpretation of neuroanatomical and neuroembryological observations are discussed.