Complex Networks We develop novel methods for the analysis of large-scale complex networks.
DNA methylation models Together with the group of Prof. Dr. Jörn Walter we develop stochastic models that describe epigenetic modifications of the DNA.
MULTIMODE (DFG) In this project we develop novel modeling and simulation methods for discrete-space biological models that exhibit multimodal behaviour.
Geobound takes a transition class model and a polynomial Lyapunov function as input and
symbolically computes the drift, i.e. a multivariate polynomial expressing the expected
change in the Lyapunov function for each state.
H(O)TA is a Matlab based tool that allows biologists to accurately
measure the methylation and hydroxylation levels at a certain locus
of the DNA and to determine the efficiencies of the enzymes that are
responsible for maintenance (Dnmt1) and de novo (Dnmt3a/b)
methylation as well as hydroxylation (Tets) at this locus over time.
The LumPy toolset implements lumping for Pair-Approximation (PA)
and Degree-Based Mean Field (DBMF) equations for contact processes
on complex networks. It reduces the large number of ODEs given by
the PA or DBMF equations by clustering them and solving instead
just a single ODE per cluster.
STAR is a tool for the stochastic hybrid analysis of Markov population models, that is, Markov processes with an underlying population structure. It efficiently computes an accurate approximation of the probability distribution at a particular time instant based on a stochastic hybrid model that combines moment-based and state-based representations of probability distributions.