Mathematics for a fundamental problem of biological information processing

The grand challenge of distributed processes is to bridge the chasm separating local...from global.... How does cellular behavior determine structure and behavior at the tissue level? How do the switching characteristics of transistors determine the behavior of a computer chip? The first of these questions is made difficult by the amorphous nature of communication between components. In both theory and simulations, the authors use large irregular networks of automata with asynchronous activity as models. The local structure is seen in the automaton's state-transition diagram. The global structure is seen in the global computation space. THEME: In entropy-reducing processes, the global attractors are homomorphic to the local slate-transition graph. The authors' investigations focus on systems of oscillators, on Turing's leopards' spot problem, and on networks of finite state automata. To the extent that global structure corresponds to global behavior, the authors' results provide a way of reducing the behavior of a tissue to that of its cells (a fundamental problem of biology).<>