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This morning we first had a talk by Pierre Borgnat on the use of data analytics for bike renting systems, which gives you access to various rhythms of a city.

We then all went for a super nice trekking around Peyresq, in pristine weather conditions: talk about perfection …

In the afternoon Pierre Borgnat gave a more technical two hours lecture on multiscale community detection and dynamic graphs. Pierre first convinced us that spectral clustering is not necessarily very good for community detection because there is no measure of partition quality and no reference to a null hypothesis (no community). This is why modularity was introduced. Modularity measures how much your graph departs from a null hypothesis where your graph is random with the same degrees. Optimizing modularity is difficult (NP complete?) but there exists a greedy algorithm (the Louvain method, what else?) that solves it, approximately, in polynomial time. Pierre then set on a challenging agenda. He first discussed cases where one really needs a multiscale definition of communities. In fact this is quite often the case since they tend to agglomerate at various scales and allow for rich interpretation. Borgnat used a wavelet transform transform on graphs to give an original and intuitive definition of what multiscale communities are. One of the niceties is that the method comes with a fast algorithm that scales up to fairly large graphs. Another important point stressed by Pierre is the definition of a stability criterion that allows to judge partitions. Pierre showed various applications and a second talk by Rasha Boulos even used the technique in genomics in a very interesting way. In the second part of his talk, Pierre discussed dynamical graph models. This is a very emerging domain where a lot remains to be done. Pierre wet our appetite with interesting ideas that allow to detect and track patterns in dynamical applications.