Table 2.

Mathematical symbols used in the description of a counting process and their interpretation in a model of neural computation

SymbolInterpretationNotes
T Duration of epochChosen by experimenter
N(T)Number of spikes from the output neuron in epoch, T Measured experimentally
N(T)〉Mean spike count from the output neuron; also read as the expectation of the spike countMeasured experimentally using repetitions of identical stimuli
Var[N(T)]Variance of spike count from the output neuronMeasured experimentally using repetitions of identical stimuli
n i(T)Number of spikes from the i th input neuron in epoch, T Unknown; we assume that input and output spike counts are the same, on average: 〈N(T)〉 = 〈n i(T)〉
λIntended spike rate of the output neuron; result of the neural computationTheoretical quantity; assumed to be constant over the epoch, so 〈N(T)〉 = 〈λT〉; this assumption can be relaxed, however; then, Embedded Image
C VISI Coefficient of variation of ISI distribution, which characterizes a renewal process: ςISIISI Theoretical quantity; can only be measured when λ is constant; for the renewal processes considered here C VISI is the same for all possible values of λ
Embedded Image Average correlation coefficient between pairs of input neuronsEstimated experimentally from pairwise recording, using repetitions of identical stimuli
  • Note the distinction between experimentally measurable and theoretical quantities.