Speed, noise, information and the graded nature of neuronal responses

How the firing rate of a neuron carries information depends on the time over which rates are measured. For very short times, the amount of information conveyed depends, in a universal way, on the mean rates only (trial-to-trial variability is irrelevant) and the cell response can be taken to be binary (although an ideal binary response would convey more). For longer times, noise as well as the graded nature of the response come into play, with opposite effects. Which times can be considered 'short' varies with the brain area considered and, possibly, with the processing speed it is required to operate at.