Time-Skew Hebb rule in a nonisopotential neuron

In an isopotential neuron with rapid response, it has been shown that the receptive fields formed by Hebbian synaptic modulation depend on the principal eigenspace of Q(0), the input autocorrelation matrix, where Qij(tau) = and xi i(t) is the input to synapse i at time t (Oja 1982). We relax the assumption of isopotentiality, introduce a time-skewed Hebb rule, and find that the dynamics of synaptic evolution are determined by the principal eigenspace of Q. This matrix is defined by Qij = integral of 0 infinity (Qij * psi i) (tau) Kij (tau) d tau, where Kij (tau) is the neuron's voltage response to a unit current injection at synapse j as measured tau seconds later at synapse i, and psi(tau) is the time course of the opportunity for modulation of synapse i following the arrival of a presynaptic action potential.