EVOLUTIONARY COMPUTING PROJECT

This report summarizes LDRD-funded mathematical research related to computer simulation, inspired in part by combinatorial analysis of sequence to structure relationships of bio-molecules. Computer simulations calculate the interactions among many individual, local entities, thereby generating global dynamics. The objective of this project was to establish a mathematical basis for a comprehensive theory of computer simulations. This mathematical theory is intended to rigorously underwrite very large complex simulations, including simulation of bio- and socio-technical systems. We believe excellent progress has been made. Abstraction of three main ingredients of simulation forms the mathematical setting, called Sequential Dynamical Systems (SDS): (1) functions realized as data-local procedures represent entity state transformations, (2) a graph that expresses locality of the functions and which represents the dependencies among entities, and (3) an ordering, or schedule according to which the entities are evaluated, e.g., up-dated. The research spans algebraic foundations, formal dynamical systems, computer simulation, and theoretical computer science. The theoretical approach is also deeply related to theoretical issues in parallel compilation. Numerous publications were produced, follow-on projects have been identified and are being developed programmatically, and a new area in computational algebra, SDS, was produced