Lecture "Complex Systems Methods"

The lecture is over.

The lecture will consist of three parts. In the first part we will deal with the identification and analysis of statistical dependencies using graphical models and methods from information theory. This corresponds to the paradigm that the complexity of a system emerges from the interactions of subsystems. Topics will include Bayesian Networks, Granger causality, Conditional mutual information and information theoretic complexity measures. In the second part we will explore a second paradigma for complexity - criticality. Keywords are phase transitions, self-organized criticality and power law distributions. In the third part we will combine both paradigms by exploring the foundation of slogans such as ”Computation at the edge of chaos“, i.e. the idea that critical states are states of maximal complexity on the one hand side and that they have particular computational power or adaptability on the other hand side.

The lecture will deal with textbook material, but also more recent research problems and results will be discussed.


A still readable overview about the early days of the ``science of complexity'' and in particular the activities at the Sante Fe Institute is provided by
Some matlab functions from the exercises