Control and computation

Many complex biological and physical systems perform computations, often upon an underlying network substrate. The network topology of these systems can support different kinds of computations, but how a system may be driven to perform one computation versus another is not well understood. Here, we frame this problem in the language of network control theory, and examine the control signals required to drive a networked system to perform a computation. After developing the framework, we analyze the energetic requirements of distinct computations, including simple mathematical operations and logic gates. We then examine which network topologies are most easily controlled for specific computations. Finally, we consider applications of this framework to real-world neural systems and mechanical systems, and discuss implications for the development of artificial neural systems and designed mechanical systems that support novel computations.