Times series analysis aims at the extraction of dynamical features of a time dependent phenomenon from observed data. This is a nontrivial task, if the corresponding phenomenon is complex in time and space. Dynamical structures unfold themselves in appropriate vector valued state spaces. The embedding procedure for the reconstruction of such state spaces from data will be reviewed, and analysis in reconstructed spaces will be illustrated by several experimental data sets. As data sources, we consider determinstic systems as well as nonlinear stochastic processes, also tolerating nonstationarity due to slow parameter variations. As an application, the prediction of turbulent gusts in surface wind will be presented. These are extreme events in a clearly complex system, which motivates us to stress the issue of extreme events on a more general level.
A nodal domain of a real vector associated with a graph is the maximal induced subgraph of a graph on which the vector does not change sign. I will talk about the number of nodal domains of trees, hypercubes and cographs.
