Connolly, Christopher and Burns, J. Brian. A State-Space Striatal Modelin Models of Information Processing in the Basal Ganglia, MIT Press, 1995.
This chapter considers the role of the striatum in computing purposeful state changes. Such state changes include, for example, movement through a maze, or an obstacle avoiding arm reach. In each of these cases, the system (arm, body, etc.) must make its way from the current state to one or more goal states, avoiding undesirable states along the way. Certain properties of the striatum make it a strong candidate for a locus of computation for this problem. Alexander et al.  present a compelling view of the basal ganglia as being involved in parallel, functionally segregated circuits. These circuits appear to run from cortex, striatum, pallidum, thalamus, and back to cortex (Graybiel 1991 ; see also Holsapple, et al. 1991 ). Using this basic architecture, this chapter attempts to examine some striatal “cross-sections” of these circuits. We postulate that these cross-sections correspond to distinct, contiguous state spaces embedded in the striatal matrix, each of which is responsible for an aspect of organism function. We also propose that the membrane potentials of cells in these regions comprise harmonic functions over each state space, and that the gradient descent of these functions produces trajectories – sequences of purposeful state changes.