Integrated Mechanisms of Anticipation and Rate-of-Change Computations in Cortical Circuits
Figure 2
Fourier Analysis of the Network Model Output Ipost upon Stimulation with White Noise Input Current Iin
In a range of low frequencies, networks with STD act as differentiators, and networks with SFA have a low-pass cutoff at neighboring frequencies.
(A) Schematic representation of the model and the computation of its transfer function H(ω) from the Fourier transforms of Iin and of Ipost
. H(ω) is an imaginary quantity that is characterized by its magnitude and its phase.
(B) Phase and magnitude of the H(ω) for mathematical derivative (top) or time-shift (bottom) operators.
(C) H(ω) phase and (D) H(ω) magnitude for Γ = 0.5, τD = 400 ms, and τCa = 80 ms in the network models of Figure 1 (same color code). To reduce the variance of H(ω), a network with N = 1,000 presynaptic neurons was used and responses to 50 different white noise realizations were averaged together. Significant phase advancement with linear increasing amplitude occurs for frequencies below 10 Hz when the network includes STD. On a single trial basis, however, only-STD networks produce unsatisfactory, very noisy Ipost (Figures 1 and 4).
(D) Every curve is scaled independently to match the initial slopes of |H(ω)| and to allow for comparisons. Inset: low-frequency range on linear scales.