  We explore statistical characteristics of avalanches associated with the
dynamics of a complex-network model, where two modules corresponding to
sensorial and symbolic memories interact, representing unconscious and
conscious mental processes. The model illustrates Freud's ideas regarding the
neuroses and that consciousness is related with symbolic and linguistic memory
activity in the brain. It incorporates the Stariolo-Tsallis generalization of
the Boltzmann Machine in order to model memory retrieval and associativity. In
the present work, we define and measure avalanche size distributions during
memory retrieval, in order to gain insight regarding basic aspects of the
functioning of these complex networks. The avalanche sizes defined for our
model should be related to the time consumed and also to the size of the
neuronal region which is activated, during memory retrieval. This allows the
qualitative comparison of the behaviour of the distribution of cluster sizes,
obtained during fMRI measurements of the propagation of signals in the brain,
with the distribution of avalanche sizes obtained in our simulation
experiments. This comparison corroborates the indication that the Nonextensive
Statistical Mechanics formalism may indeed be more well suited to model the
complex networks which constitute brain and mental structure.
