Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will review methods to solve those equations, and notably methods to draw with guarantees the real solutions of an under-constrained system of equations modeling the singularities of a robot.[-]

Extreme events are of primarily importance for understanding the impact of climate change. However, because they are too rare and realistic models are too complex, traditional deep neural networks are inefficient for predictions. We cope with this lack of data using rare event simulations. From the best climate models, we oversample extremely rare events and obtain several hundreds more events than with usual climate runs, at a fixed numerical cost. Coupled with deep neural networks this approach improves drastically the prediction of extreme heat waves.[-]