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.
Cascade processes have been proven useful models for such diverse phenomena as epidemic spreading, the propagation of information in social media or financial systemic risk. The central question is: How big is the risk that a few initial infections spread through a network and result in an epidemic outbreak? Common answers are based on estimates of the average cascade size as proxy for systemic risk. In the past decade, substantial progress has been made to calculate it efficiently by Mean Field Analysis and Belief Propagation. Yet, in finite networks, this average does not need to be a likely event. Instead, we find broad and even multi-modal cascade size distributions. These occur also in large systems and far away from phase transitions. To show this, we derive efficient algorithms to compute the probability distribution of the finite cascade size and conditional infection probabilities of nodes for a large class of models. These have multiple applications, for instance, in learning node embeddings, solving variants of influence maximization, detecting the source of an epidemic outbreak, or inferring the parameters of a cascade model.