This is a short introduction to Kolmogorov complexity and information theory. The interested reader is referred to the literature, especially the textbooks [CT91] and [LV97] which cover the fields of information theory and Kolmogorov complexity in depth and with all the necessary rigor. They are well to read and require only a minimum of prior knowledge. Kolmogorov complexity. Also known as alg...

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system’s first exit from the interior of the unstable orbit occurs, typically displays the phenomenon of cycling: The distribution of first-exit locations is transl...

A periodically driven lattice with two commensurate spatial periodicities is found to exhibit super metallic states characterized by enhancements in wave packet spreading and entropy. These resonances occur at critical values of parameters where multi-band dispersion curves reduce to a universal function that is topologically a circle and the effective quantum dynamics describes free propagatio...

The classical approach to using utility functions suffers from the drawback of having to design and tweak the functions on a case by case basis. Inspired by examples from the animal kingdom, social sciences and games we propose empowerment, a rather universal function, defined as the information-theoretic capacity of an agent’s actuation channel. The concept applies to any sensorimotoric appara...