FIG. 4. (Color online) Time-scale invariance emerges from criterion time noise in the SBF model.
(A) Time-scale invariance emerges spontaneously in a nosy SBF-sin model; here the two criteria are T = 30s and T = 90s. The output functions (continuous lines) were fitted with Gaussian curves (dashed lines) in order to estimate the position of the peak and the width of the output function. (B) In an SBF-sin model, the standard deviation increases linearly with the criterion time in all four trials shown with different symbols. (C) In an SBF-ML implementation, low levels of Gaussian noise (solid rectangles represent σT = .1% and circles σT = 1%) produce an almost constant standard deviation of the output function similar to noise free case. At high enough levels of noise (solid triangles represent σT = 10%), the SBF-ML model with criterion time variance produces a standard deviation σo that increases linearly with the criterion time T, which is the hallmark of time-scale invariance.