Date depot: 4 avril 2021 Titre: Characterisation of multiscale geometry in brain networks Directeur de thèse: Mario CHAVEZ (ICM) Domaine scientifique: Sciences et technologies de l'information et de la communication Thématique CNRS : Non defini Resumé: Complex networks have been increasingly used to analyse and model brain connectivity derived from experimentally obtained data. Topological properties, such as the node centrality, efficiency and modularity have been shown to reveal complementary information on the brain functioning in healthy and pathological conditions. However, what is the latent structure behind the brain network properties is still poorly understood. Modern dimensionality reduction methods learn nonlinear similarities/proximities (that can be also interpreted as dissimilarities/distances) between points distributed over a hidden manifold in a multidimensional feature space, in order to preserve, embed (map) and visualize them in a low-dimensional reduced space. Such embedding methods can map brain networks in Euclidean spaces, but they are unable to fully explain the structural organization of brain connectivity, which motivates the quest for a latent geometry of the brain connectivity. The question of whether it exists a hidden geometry from which real complex networks emerge has attracted the attention of the community lately, and is getting more and more ground. The possibility to find an effective congruency between network characteristics and its representation in a latent geometric space offers the possibility to understand the reason behind its structure and function at a more fundamental level, and address the study of complex phenomena taking place in these systems in a novel and promising framework. This project aims to explore non-Euclidean geometries to represent complex brain networks, and to work in the most appropriate hidden geometric space representation of it to unveil properties of the system in a complementary and coherent way.