Dependence of cerebellar module information storage parameters on properties of mossy fibers-Granule cells connection matrix

An algorithm for the evaluation of the width of a nonzero elements diagonal strip (NEDS) for any matrix has been proposed. The algorithm includes iterative renumeration of the lines and columns of a matrix in order to obtain a matrix possessing the narrowest possible width of the NEDS that is invariant to the initial form of the matrix. The authors consider the stochastic distribution function of a number of excited granule cells when different randomly chosen patterns of activity are imposed on mossy fibers. The dependence of this distribution function on the minimal width of the NEDS is demonstrated. In considering information learning and its recall from cerebellar modules, the probabilities of false memory and inability to learn some concrete patterns were calculated as a function of Purkinje cell threshold and parameters of the network. In principle, the learning capabilities of a cerebellar module increase with NEDS width