We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDPs polarity, functional loops are
formed or eliminated in networks driven to normal spiking conditions by random, partially correlated inputs, where functional loops comprise weights that exceed a non-zero threshold. We further prove that STDP is a form of loop-regulating plasticity for the case of a linear network comprising random weights drawn from certain distributions. Thus a notable local synaptic learning rule makes a specific prediction about synapses in the brain in which standard STDP is present: that under normal spiking conditions, they should participate in predominantly feed-forward connections at all scales. Our model implies that any deviations from this prediction would require a substantial modification to the hypothesized role for standard STDP. Given its widespread occurrence in the brain, we predict that STDP could also regulate long range synaptic loops among individual neurons across all brain scales, up to, and including, the scale of global brain network topology.
For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongl
y stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian behavior: {sl all} degrees of freedom achieve a close balance of excitation and inhibition and become critical in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex breakout dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense.
