Table 1. Notation used in the text.

Symbol	Description
	Membrane potential, membrane time constant, leak reversal potential, and noise intensity of cell .
	Mean and standard deviation of the background noise for cell .
	Membrane potential threshold, reset, and absolute refractory period for cells.
	Spike generating current, soft threshold and spike shape parameters for the IF model [25].
	Synaptic input from other cells in the network, and external input to cell .
	Synaptic time constant and delay for outputs of cell .
	Spike train of cell .
	The synaptic weight, proportional to the area under a single post-synaptic current for current-based synapses.
	The synaptic kernel - equals the product of the synaptic weight and the synaptic filter for outputs of cell .
	The cross-correlation function between cells defined by .
	Spike count for cell , and spike count correlation coefficient for cells over windows of length .
	Stationary rate, linear response kernel and uncoupled auto-correlation function for cell j.
	The interaction kernel - describes how the firing activity of cell is perturbed by an input spike from cell . It is defined by .
	The order approximation of the activity of cell in a network which accounts for directed paths through the network graph up to length ending at cell , and the cross-correlation between the order approximations of the activity of cells .
	is the Fourier transform of with the convention