Abstract: | Cross-correlation functions, RXY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, RXY(t,τ) = fU θ-h(τ), t + τ] {h′(τ) + EU u′(t + τ)]} for positive values of this quantity, where fU(u,t) is the probability density function of U(t) and EU u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in RXY(t,τ) for a neuron subjected only to excitation. (3) For large τ, RXY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) RXY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time. |