Combinatorial Models for the Dynamics of Complex Decision
Systems
Combinatorial Models for the Dynamics of Complex
Decision Systems
Michael Coombs, Reinhard Laudenbacher, and Karen Schlauch
Physical Science Laboratory, Mathematical Sciences, New Mexico State University
One important factor which determines the dynamics of a decision system
is the distribution of ``influence'' in the network, understood quite
broadly. This talk will describe an approach to capturing this influence
structure with new combinatorial and algebraic tools.
The space of possible states of the system does usually not carry
any structure beyond that of a directed graph. We enrich this structure
by constructing a discrete analog of a vector bundle on this space, that
captures the local flow of influence. Algebraic invariants of this discrete
vector bundle give structural properties of the network, which are related to
its dynamics. We will illustrate these ideas with experimental results
for Boolean networks.