First abstract (Lucie Brolon):

When an infectious agent enters the body, it is detected by dendritic cells (DCs), which then emit biochemical signals to initiate an immune response, inducing the differentiation of T lymphocytes (LTs). Each signal needs to be analyzed in the context in which it was generated: LTs absorb a combination of signals emitted by DCs, which may be different in nature and may be emitted simultaneously by DCs. We use several decision-tree based algorithms to analyze this cellular communication and compare them using a simulation study. We then use them on a preliminary real data set.

Second abstract (Ivan Hasenohr):

It is customary to design a control system in such a way that, whatever the chosen control satisfying the constraints, the system does not enter so-called unsafe regions. This work introduces a general computer-assisted methodology to prove that a given linear parabolic control system with compact constraints avoids a chosen unsafe set. Relying on support hyperplanes, we devise a functional such that the property of interest is equivalent to finding a point at which the functional is negative. Actually evaluating the functional first requires time- and space-discretisation. We thus provide explicit, fine estimates for finite elements discretisation. Second, computations lead to roundoff errors, which are dealt with by means of interval arithmetic. The control of both error types then leads to rigorous, computer-assisted proofs of non-reachability of the unsafe set.