Single neuron computations based on the rational function model

Neurons are basic processing elements (PEs) of neural networks. For neural network researchers, understanding the computations performed by real neurons is essential to the design of the artificial neural networks (ANNs) which are biologically plausible and computationally powerful.; This thesis focuses on phase analysis to explore the potential of 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 and the analysis of arithmetic operations, the prototypes of logic operations are constructed with their input and output ranges. Then 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 both arithmetic and logic operations are also discussed for the connections between neurons in different layers. Software simulation of the neurons based on the rational function is also presented.; Our theoretical studies and software implementations indicate that the single neuron local rational arithmetic and 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.