The construction of a simultaneous functional order in nervous systems. I. Relevance of signal covariances and signal coincidences in the construction of a functional order.

We have developed two algorithms that construct a simultaneous functional order in a collection of neural elements using purely functional relations. The input of the first algorithm is a matrix describing the total of covariances of signals carried by the members of the neural collection. The second algorithm proceeds from a matrix describing a primitive inclusion relation among the members of the neural collection that can be determined from coincidences in their signal activity. From this information both algorithms compute a partial functional order in the collection of neural elements. Such an order has an objective existence for the system itself and not only for an external observer. By either merging individual neurons or recruiting previously unspecified ones the partial order is locally transformed into a lattice order. Thus, the simultaneous functional order in a nervous net may become isomorphic with a geometrical order if the system has enough internal coherence. Simulation experiments were done, both for the neuron-merging and the neuron-recruitment routines, to study the number of individuals in the resulting lattice order as a function of the number of individuals in the underlying partially ordered set.