Collective dynamics of cortical columns and the distribution of dominance periods R Cao1, A Pastukhov2, J Braun2, M Mattia3 |
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1Complex Systems Modelling, Istituto Superiore di Sanita, Italy |
| We propose a novel analytical framework for the collective dynamics of cortical columns. We assume that (i) individual columns transition spontaneously between active and inactive states, (ii) stimulation increases likelihood of active states, (iii) cooperative percepts (e.g., coherent motion) integrate activity over a population of columns, and (iv) perceptual onset occurs when population activity exceeds a fixed threshold. This framework constitutes a known stochastic process, for which we obtain analytically all moments of the distribution (FPTD) of first-passage-times (times between stimulation onset and threshold crossing). Our analysis predicts mean and shape of FPTD as a function of spontaneous, stimulated, and threshold levels of activity. In low-threshold regimes, stimulated levels alter mean, but not shape, of the FPTD. This is because the mean is mainly a ‘local effect’ (coupling between stimulation and active times), whereas the shape is a ‘collective effect’ (spontaneous and threshold levels of activity). Intriguingly, the predicted dissociation is mirrored by the empirical distribution of dominance periods in multi-stable displays, where stimulation alters the distribution mean ten-fold, but leaves distribution shape almost unchanged (coefficient of variation ~ 0.5, skewness ~ 1.0). We conclude that the characteristic stimulus-dependence of dominance periods may reflect the collective dynamics of cortical columns. |
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