Séminaire Jeunes chercheurs (Théo Leblanc, jeudi 3 avril 2025)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 3 avril 2025 à 17h en salle A707. Nous aurons le plaisir d'écouter Théo Leblanc (CEREMADE), qui nous parlera de

Hawkes and Autoregressive processes in Neuroscience

Abstract
In this talk we present a special class of point processes: Hawkes processes and focus on how Hawkes processes can be used in Mathematical Neuroscience to model functional connectivity. In neuroscience, functional connectivity can be seen as an ensemble of interactions between brain oscillations (rhythms) and individual neuronal activity (spikes). Neuronal activity can be modeled by a multivariate Hawkes process. The points of the Hawkes process correspond to the spiking times of each neurons and the spiking activity at time t depends on past spikes of the different neurons. Brain rhythms, another important quantity about brain activity, can be defined as the wavelet coefficients of the LFP (local field potential) signals and are therefore treated as discrete sequences. Autoregressive equations are the standard way of modeling interactions between brain rhythms. We introduce a coupled model combining both Hawkes and AutoRegressive processes to describe at once all possible interactions between neurons and brain rhythms. We present theoretical results and a statistical method based on the LASSO to infer functional connectivity.