Benjamin Merkt
Gauge invariance plays an important role in many physical theories. In a broader sense it can be defined as the invariance of an observation with respect to changes of internal variables. In cell biology, one often faces a similar problem. Due to limitations in the available experimental data, usually only a small fraction of the relevant protein concentrations can be measured. To model cellular reaction networks, it is common to use ordinary differential equations (ODE). Therefore, in order to find gauge invariances in these systems, Lie-group theory can be applied. In many cases such an analysis yields symmetry transformations on the internal variables, i.e. the ODE states corresponding to the cellular concentrations, which do not affect the observed quantities. Thus, the log-likelihood functional is invariant under these transformations. The symmetries can then be used to reduce the number of parameters.
Time & Venue
Friday, 17th of January 2014, SR 404, Institute of Mathematics