Many natural processes and even modern human-designed systems exhibit very complicated behaviour. Lorenzo Sella of the Centrum Wiskunde & Informatica (CWI) has developed new methods to obtain a better understanding of these. He will defend his thesis 'Computation of symbolic dynamics of low-dimensional maps’ on 1 December at the Vrije Universiteit Amsterdam. His results may be of interest for researchers in many different fields, such as control engineers that want to regulate complex systems and system biologists that want to understand such systems like chemical cell reactions
Sella has developed mathematical methods for computing ‘discrete abstractions’ of dynamic processes. These provide a simple description of the most important phenomena occurring during the process, and are very useful in gaining insight into the process of interest. For example, in studying the chemical reactions in a human cell, it is often not necessary to know the exact concentrations of the various proteins involved, but only whether the concentration is high or low, and on this basis to study the influence on the further progress.
The same methods developed by Sella can be applied for the verification of technical systems. For example, they could be used to determine whether the system behaves more-or-less as expected, and performs its task without failures occurring. But not even mathematic analysis can uncover all properties of complex natural processes. For example, Sella showed in his thesis that for complex systems, it is usually impossible to accurately compute a numerical measure of just how complex the system actually is, even given a precise mathematical model.