Stochastic formulation of neural interaction (Q1061638)

Starting from basic physiological evidence, stochastic equations are formulated for the description of neural interaction. The formulation is based upon the deterministic linear spatio-temporal integration of action potentials into generator potentials. On the other hand, the action potentials are considered as stochastic all-or-none variables whose probability of generation depends only on the local instantaneous value of generator potential and generator current. For a model in continuous time, the action potentials can be appropriately modelled by a point process; for the description in discrete time, a switching process appears more suitable. Properties of the trajectories representing neural dynamics in state space are indicated. A neural partition function is defined and shown to be related to a statistical description of the neural activity pattern. The relevance of the mathematical formulation is indicated for the relation of neural correlation and synaptic connectivity.