Definition and properties of noise. Graphs show properties of three different noise signals. Middle row of graphs shows Gaussian white noise. That is, the value at each time point is randomly drawn from a Gaussian distribution (shown on far left). Power spectrum shows that the signal contains equal amounts of power at all frequencies from 0 to 2500 Hz. Top row shows low pass filtered noise. Distribution of signal values (far left) is identical to the white noise case, but values at any time point are correlated with those at other time points, resulting in slower fluctuations and a power spectrum that is reduced at high frequencies. Bottom row shows white noise of a lower amplitude than in the middle graph. Distribution of stimulus values (far left) is narrower than for the middle row, but the power spectrum is flat.

Noisy inputs cause reliable spiking in vitro and in vivo. (a) Left teady-state current injection into a cortical pyramidal cell in vitro results in trains of action potentials shown as voltage traces (top) or spike rasters (bottom). On different trials the first spike is evoked at the same time on each trial, but subsequent spikes are unreliable. Right: injection of fluctuating current causes the cell to spike reliably throughout the spike train. (b) In vivo recordings from cortical area MT shows reliable spiking in response to fluctuating (but not steady-state) visual motion stimuli. (a) Adapted from Mainen et al. [66]. (b) Adapted from Buracas et al. [67].

The phase resetting curve and noise-induced oscillatory synchronization. (a) Pulse-like stimulus delivered to an oscillating neuron changes the timing of the next action potential. In this case, the action potential is delayed by an amount Δ(θ). The delay or advance of the next action potential (Δ(θ)) is determined by the phase at which the stimulus arrives (θ). (b) Effect of single pulse-like input on synchrony in a network of model neurons. Spike rasters show action potential times in a network of uncoupled neurons (modeled as quadratic integrate and fire) [14,68]. Rasters are arranged in order of firing times, generating the diagonal pattern. Pulse-like input at 15 ms advances some spikes and delays others, transiently disrupting the oscillations of some cells and generating more synchronous spiking across the population. Bottom shows histogram of number of spikes per bin. Spikes are uniformly distributed before input is delivered at 15 ms, and clustered after.