Network
A thousand leaky integrate-and-fire cells, 800 excitatory and 200 inhibitory, sparsely wired. The spike shape is thrown away and only the timing kept — which is the trade that makes a population of this size tractable at all.
With four excitatory cells per inhibitory one, a ratio of 4 is exact balance. Below it the network runs away; well above it, it falls silent.
Fifteen millivolts separate rest from threshold and the membrane time constant is 20 ms, so above about 0.75 the MEAN drive alone reaches threshold and the cells become clocks.
Mean rate
8.0Hz
Irregularity (CV)
0.59
Cells firing
100%
Spike raster
Gold excitatory, blue inhibitory. What a balanced network looks like is exactly this: no vertical stripes. A stripe is the whole population firing together, which is a seizure and not a circuit.
The STDP window
Bi & Poo (1998). Presynaptic spike BEFORE postsynaptic — the causal order, right of centre — strengthens the synapse; the same interval reversed weakens it. The window is tens of milliseconds wide, and that narrowness is what makes it detect causality rather than correlation.
And it reverses with rate
- 5 Hz, presynaptic leading by 5 ms+0.297
- 10 Hz, presynaptic leading by 5 ms+0.273
- 20 Hz, presynaptic leading by 5 ms+0.176
- 40 Hz, presynaptic leading by 5 ms-0.037
The same causal pairing potentiates at low rates and DEPRESSES at 40 Hz. This is not a bug and it was not designed in: with every pre spike paired against every post spike, the depression window at 33.7 ms is twice as wide as the potentiation window at 16.8, so shortening the interval accumulates anti-causal partners faster than causal ones. Much of the literature uses nearest-neighbour pairing to avoid it; this keeps the all-to-all form because it is what Bi and Poo's own fit describes.
Comparing a model cell with a person
The coefficient of variation above is the standard measure of firing irregularity: 0 is a metronome, 1 is a Poisson process. The same statistic can be computed over any sequence of intervals, including human reaction times — which is what the Spike Train exhibit did, and where this comparison came from.
Carried over from that exhibit verbatim, because next to a page computing real spike statistics on a real model cell it is the sentence that stops a reader drawing the wrong conclusion: these are the same formulas applied to a different kind of interval data, and that is not a claim that reaction times are neural spikes.