Material to the manuscript “ Connectomic Constraints on Computation in Feedforward Networks of Spiking Neurons ”

Online Resource A: Relationship of the abstract neuron model to some widely-used neuron models Here, we demonstrate that the properties that our abstract model of the neuron is contingent on are satisfied, up to arbitrary accuracy, by several widely-used neuron models such as the Leaky Integrate-and-Fire Model and Spike Response Model. Leaky Integrate-and-Fire Model Consider the standard form of the Leaky Integrate-and-Fire Model: τm du dt = −u(t) + RI(t) (1) where τm = RC. When u(t (f)) = v, the neuron fires a spike and the reset is given by u(t (f) + ∆) = ur, where v is the threshold and ∆ is the absolute refractory period. Suppose an output spike has occurred at timê t − ∆, the above differential equation has the following solution: u(t) = ur exp(− t − ˆ t τm) + 1 C t−ˆt 0 exp(− s τm)I(t − s)ds (2) Suppose I(t) = Σ j w j Σ i α(t − t (i) j) and α(·) had a finite support. Then, it is clear from the above expression that the contribution of the previous output spike fired by the present neuron as well as the contribution of input spikes from presynaptic neurons decays exponentially with time. Therefore, one can compute the membrane potential to arbitrary accuracy