Chaitanya Ekanadham 1 Neural coding basics

1 Neural coding basics 1.1 Definitions 1. Response function ρ(t) = j δ(t − t j) where t j are the spikes 2. Firing rate r(t) = lim ∆t→0 1 ∆t t+∆t t ρ(s)ds 3. Spike count n = T 0 ρ(t)dt 4. Average firing rate˜r = 1 T T 0 ρ(t)dt = n T 5. Tuning curve f (s) = avg firing rate given a parameterized stimulus s (typically plotted as a histogram and then fit to some functional form) 6. Stimulus/Response correlation Q rs (τ) = 1 T T 0 r(t)s(t + τ)dt 7. Spike-triggered average C(τ) = 1 n T 0 ρ(t)s(t − τ)dt ≈ 1 n T 0 r(t)s(t − τ)dt 8. Stimulus autocorrelation Q ss (t) = 1 T T 0 s(t)s(t + τ)dt 9. Response autocovariance/autocorrelation Q ρρ (t) = 1 T T 0 (ρ(t) − ˜ r)(ρ(t + τ) − ˜ r)dt 10. Rate code-code in which all stimulus information is conveyed via the firing rate function r(t) which does not vary at faster timescales than the stimulus s(t) (Note: a rate code can still be very spike-time-dependent if the stimulus is very fast-varying thus inducing a fast-varying rate-the key is that if the stimulus is slow-varying than the rate function should not be so time-sensitive). 11. Pulse/temporal code-code in which information is carried in variations of the rate function that are on shorter timescales than the fastest stimulus variation.