María A. Altahona-Medina

Inter-saccadic times or eye fixation durations (EFDs) are relatively stable at around 250 ms, equivalent to four saccades per second. However, the mean and standard deviation are not sufficient to describe the frequency histogram distribution of EFD. The exGaussian has been proposed for fitting the EFD histograms. The present report tries to adjust a competition model (C model) between the saccadic and the fixation network to the EFD histograms. This model is at a rather conceptual level (computational level in Marr’s classification). Both models were adjusted to EFD from an open database with data of 179,473 eye fixations. The C model showed to be able, along with exGaussian model, to be compatible with explaining the EFD distributions. The two parameters of the C model can be ascribed to (i) a refractory period for new saccades modeled by a sigmoid equation (A parameter), while (ii) the ps parameter would be related to the continuous competition between the saccadic network related to the saliency map and the eye fixation network, and would be modeled through a geometric probability density function. The model suggests that competition between neural networks would be an organizational property of brain neural networks to facilitate the decision process for action and perception. In the visual scene scanning, the C model dynamic justifies the early post-saccadic stability of the foveated image, and the subsequent exploration of a broad space in the observed image. The code to extract the data and to run the model is added in the ^{Supplementary Materials}. Additionally, entropy of EFD is reported.

The basic functioning of the central nervous system is based on the opening and closing of ionic channels in the membranes of neurons. The behavior of ionic channels is considered to be a random process with an exponential probability distribution function. The central limit theorem implies that the mean of the sum of random variables generates a distribution in which the new variable tends to be normally distributed. The theorem implicitly implies that randomness can be embedded in a certain probability distribution but does not disappear. The present report will explore the possible implications for the functioning of nervous system and behavior of the constituent neural randomness. The possible functionality of “noise” to increase the exploratory space of nervous and behavioral systems will be considered.