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Dendritic Pooling of Noisy Threshold Processes Can Explain Many Properties of a Collision-Sensitive Visual Neuron
Fig 2
How noise interacts with maximum detection.
This figure shows how the numerical detection of the global maximum 
is affected by adding noise to the η-function, g3(t), and 𝒮(g3). To this end, the root mean square error (RMSE) between 
and the theoretical (i.e. noise-free) tmax is determined across 999 trials. The RMSE is computed as a function of noise amplitude σ (abscissae) and the halfsize-to-velocity ratio l/v (ordinates). Brighter (“hotter”) colors denote bigger RMSE values (see colorbar; units in milliseconds). Noise is added as follows. Let ξ be a normal-distributed random variable with mean zero and standard deviation one. Then, (a)η(t) + σξ is the “noisified” η-function (with δ = 0 and α = 4.7), (b)shows the RMSE for g3(t) + σξ, and (c) 𝒮(g3) + σξ (with a = 1 in Eq (8)). The curves of η(t), gp(t) and 𝒮(gp) become flatter for higher halfsize-to-velocity ratios (cf. Fig 1). In addition, the curves of gp(t) become flatter for increasing p, and the curves of 𝒮(gp) get flatter for decreasing values of a and p, respectively. Flatter curves are associated with an increased RMSE. Although g3(t) + σξ is associated with higher RMSE values than η(t) + σξ, the completely “decoded” function 𝒮(g3) has a better overall robustness against additive Gaussian noise than η(t). For each value of l/v, g3(t) and 𝒮(g3) were re-scaled before noise was added, in order to match the range of η(t), and thus normalize the RMSE. For all figure panels, tc = 0.5s and l = 0.06m.
doi: https://doi.org/10.1371/journal.pcbi.1004479.g002