A central problem in the study of complex systems is to identify hierarchical and intertwined dynamics. A hierarchical level is defined as an aggregation of the system's variables such that the aggregation induces its own closed dynamics. In this paper, we present an algorithm that finds...

We present a method for identifying coarse-grained dynamics through aggregation of variables or states in linear dynamical systems. The condition for aggregation is expressed as a permutation symmetry of a set of dual eigenvectors of the matrix that defines the dynamics. The applicability of the...

In this paper, we introduce a method for determining local interaction rules in animal swarms. The method is based on the assumption that the behavior of individuals in a swarm can be treated as a set of mechanistic rules.The principal idea behind the technique is to vary parameters that define...