The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue). If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.
The seminar is open to public and does not require any form of registration.
Logical (discrete: Boolean or multivalued) models have been used to study biological regulatory networks over the last 40 years. The increasing size of the networks of interest calls for formal methods for their dynamical analysis.
We proposed a model reduction method, to construct "simpler" version of the models by taking out selected components and integrating their role in the functions of their targets. We showed that this rewiring of the model is only possible for components which are not self-regulated, and that this condition ensures the preservation of the attractors. While this reduction can not create additional reachability properties, it can, in case of conflicts, remove some of the existing ones.
To study the basins of attraction, we propose the construction of a "reversed" model regarding the asynchronous dynamical behaviour: the successors of the states of a reversed model correspond to their predecessors in the original one. While the reversal can be generalized only to a particular class of multivalued models, we show how to use model booleanization to study the reversed asynchronous dynamics of any model. The study of the reversed dynamics then facilitates the identification of the basins of attraction, assuming that we already know the attractors. We can further compute "strong" and "weak" basins (from which we can respectively reach a unique or multiple attractors), as well as their "frontiers", i.e., the sets of states such that the reachable attractors are different from the attractors reachable from neighbouring states (predecessors or successors)