On the properties of time trajectories learned by the cerebellar cortex

The cerebellum has a role in motion control and coordination, but the mechanisms of movement coordination are unknown. Enough physiological data are known on the cerebellar cortex to build a realistic model of its function. The interpretation of Chauvet and Chauvet (1999), hierarchically and mathematically oriented, answers the main issue of the functional relation between the regular, homogeneous observed neural tissue and the high capacity of movement regulation. This approach led to a mathematical definition of the functional unit of the cerebellum based on the stability of its dynamics. Here, we extend the work of Chapeau-Blondeau and Chauvet (1991), to explore the efficiency and the capacity of the cerebellar cortex to learn and memorize trajectories, i.e. time series patterns, taking into account its anatomical features. This is important because the field theory we have conceived involves the whole geometry of the system, thus the role of the delays of propagation between any cells, and because we have not yet any idea of the number of possible learned patterns. Using the most recent anatomical data on the cerebellum, the aim in this paper is: (i) to build an element of the cerebellar cortex using a semi-real neural network and an object-oriented implementation, (ii) to study the role of the most important parameters on the capacity of the cerebellar cortex to learn and retrieve temporal patterns, and (iii) to see to what extent the results of Chapeau-Blondeau and Chauvet may be usable