Mathematical Foundations of Bioinformatics
We investigate the generic principles underlying distributed computation in biological systems, by identifying the fundamental properties of biophysical phenomena (e.g. synchronization) and relevant mathematical/computational models (e.g. Cellular Automata).
As one specific question, we ask what behaviors can be exhibited by a given biological/biochemical system upon variation of the parameters. In this context, shrimps or swallow-tails are generic, characteristic parameter space regions that separate fixed stable periodic behavior from irregular behavior. A smooth feature-mapping will reflect in feature space what is observed in parameter space, which may cause severe problems for standard bioinformatics approaches (e.g. k-means or Ward clustering).
We investigate the generality of this problem and search for methods that could remedy this situation (e.g. better clustering algorithms). As an application, we ask why the recognition of sounds (e.g. of phonemes) is so difficult for artificial devices, compared to humans.