Error-correction in distributed computational networks using self-organized collective dynamics

Dynamical processes on networks often exhibit self-organized collective behavior in which the activities of large numbers of nodes spontaneously synchronize without the intervention of a central processing unit (CPU). Sometimes such a synchronized state can be interpreted as ``performing a useful task.'' For concreteness, suppose the nodes of the network can take on state values 0 or 1. Initially, the network has some heterogeneous distribution of states, in which the majority state is assumed to be ``correct'' and the minority state is an ``error.'' The task is to identify which state is in the majority and to change all of the minority states to the correct value---without the assistance of a CPU. We show how the nodes can be wired together in a locally-connected architecture to produce a spatio-temporal dynamical system whose attracting state is all 0s or all 1s, depending on which was initially in the majority. We discuss a specific application for such a network that could potentially be of use aboard spacecraft in hostile radiation environments.