**A:** The top (red) spike train represents vestibular input

and the bottom (blue) spike train represents inhibitory cerebellar input

. The green curve shows an iSTDP profile (corresponding to a difference of Gaussians kernel

as described in Methods) chosen to demonstrate both LTP and LTD lobes clearly. The total contribution of a given vestibular spike, for example the one extended by the red dotted line, to synaptic weight change is calculated as follows: its timings

with respect to all cerebellar spikes are determined. The contribution of each of these spike pairs to weight change is proportional to

(equation (3)), these values are shown graphically as the blue segments under the iSTDP profile centered at the chosen vestibular spike. The sum of all these segments is the weight change ‘caused’ by that vestibular spike.

**B:** A sinusoidal vestibular input modulating at 3 Hz, represented as a variation in firing rate with mean rate 30 Hz and amplitude 20 Hz.

**C:** A raster plot of 200 different Poisson coded samples of the sinusoidal signal (for Poisson coding the probability of a spike in a short interval

is

where

is the firing rate to be coded). It is clear that the coding scheme is asynchronous, i.e. the timing of individual spikes is not well-determined.

**D:** A histogram of all interspike intervals τ (between vestibular and cerebellar spikes, see Methods) for a single 50 s

input pair modulated in phase at 3 Hz and Poisson coded as in . Despite the fact that individual spikes are not precisely timed, there is a clear modulation of the ISI histogram at 3 Hz with a peak at zero ISI. The experimentally constrained iSTDP profile from is overlaid on the histogram.

**E:** Cumulative weight change calculated for 20 pairs of 50 s samples of vestibular and cerebellar input. There is a stochastic but consistent weight decrease. The mean weight change (dark blue curve) is also shown.

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