It is often difficult to understand how simple individual parts interact and integrate to form complex global behaviour. Examples include interacting particle systems and coupled oscillators, with applications such as the dynamics in living cells, human (business) behaviour, and datamining. One may approach such phenomena head-on by writing down models that incorporate the underlying mechanisms or processes, and that hopefully capture the dynamics displayed in reality. Alternatively, complexity may be present in highdimensional datasets and the goal is to find patterns within this. Particularly in medicine and business, opportunities for new statistical methods and datamining abound. The Department is active on both these analytical and stochastic fronts, and research varies from the very abstract to the very applied.
More and more applied problems studied at the VU arise from biology, such as regulation of yeast glycolysis, cell growth models, and collective behaviour in social insects. Mathematically, the problems are two-fold. In many cases, such as in ant colony organization, the main question is how to construct models that are both meaningful and open to analysis. In other cases, such as yeast glycolysis, the models are often large systems of differential equations. The main goal now is to capture the qualitative behaviour of the dynamics with reduced models, using scaling arguments or other model reduction techniques.
In statistics, our main partner for collaboration is the VU medical center. New techniques are being developed on several fronts, such as extracting information from PET or MRI scanners, finding genes that are associated with diseases, using twins in medical trials, and extracting the connectivity between neurons in neuronal populations. Another field of application for stochastic methods is business analytics. Finding needles in a haystack is a common problem in many business situations. An example is the detection of buying patterns in the data available through client databases (e.g. linked to reward cards or web shops). Such patterns can for instance be used to formulate intelligent recommendations to shoppers.