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Integrate-and-fire (IF) neurons have found widespread applications incomputational neuroscience. Particularly important are stochastic versions ofthese models where the driving consists of a synaptic input modeled as whiteGaussian noise with mean $\mu$ and noise intensity $D$. Different IF modelshave been proposed, the firing statistics of which depends nontrivially on theinput parameters $\mu$ and $D$. In order to compare these models among eachother, one must first specify the correspondence between their parameters. Thiscan be done by determining which set of parameters ($\mu$, $D$) of each modelis associated to a given set of basic firing statistics as, for instance, thefiring rate and the coefficient of variation (CV) of the interspike interval(ISI). However, it is not clear {\em a priori} whether for a given firing rateand CV there is only one unique choice of input parameters for each model. Herewe review the dependence of rate and CV on input parameters for the perfect,leaky, and quadratic IF neuron models and show analytically that indeed inthese three models the firing rate and the CV uniquely determine the inputparameters.

Are the input parameters of white-noise-driven integrate-and-fire neurons uniquely determined by rate and CV?