Time series analysis
Time series of complex systems (e.g. the power load of large infrastructure systems) are in general the result of deterministic as well as stochastic processes. However, quite often, what looks on a first glance as noise is in fact to a large part the result of internal deterministic dynamics. Modern mathematics provides a number of tools (such as the determination of local expansion coefficients) that enable to reveal important aspects of this internal dynamics.
A very obvious and straightforward way to exploit knowledge about the internal dynamics is of course prediction. However, the prediction horizon is often disappointingly short. But there is another potential use: Quite often, there exist models of infrastructure systems. The challenge is to validate such models (experiments are difficult or impossible and initial conditions only partially knowns). The knowledge of characteristic parameters (such as local expansion coefficients) in the real system enables a comparison with the according parameters of the simulation. A sufficiently close similarity is a strong indication that the model represents the reality at least with respect to relevant dynamic aspects. ACSS has extended experience in this type of studies and we are ready to support modelers with our methods from dynamical systems theory.