Logic operations based on single neuron rational model

This paper focuses on phase analysis to explore the single neuron local arithmetic and logic operations on their input conductances. Based on the analysis of the rational function model of local spatial summation with the equivalent circuits for steady-state membrane potentials, the prototypes spatial summation with the equivalent circuits for steady-state membrane potentials, the prototypes of logic operations are constructed. A mapping from a partition of input conductance space into functionally distinct phases is described and the multiple mode models for logic operations are established. The transitions from output voltage to input conductance in logic operations are also discussed for the connections between neurons in different layers. Our theoretical studies and software simulations indicate that the single neuron local rational logic is programmable and the selection of these functional phases can be effectively instructed by presynaptic activities. This programmability makes the single neuron more flexible in processing the input information.