The successful applicant will work with Prof. M. Ángeles Serrano and Prof. Marián Boguñá at the Department of Condensed Matter Physics of the University of Barcelona and UB Institute of Complex Systems (UBICS).

Structural brain networks are spatially embedded networks whose architecture has been shaped by physical constraints and functional needs throughout evolution. Euclidean space is typically assumed as the natural geometry of the brain. However, distances in hyperbolic space offer a more accurate interpretation of the structure of connectomes across species, including multiscale self-similarity in the human brain. Implications extend to debates, like criticality in the brain, and applications, including tools for brain simulation.

We introduced a geometric renormalization technique for complex networks that allows us to explore complex systems at different resolution levels. Using it, we found that the connectivity in complex networks at different length scales is regulated by the same principles and looks self-similar. Strikingly, the same ideas can be applied to explain the self-similar growth of complex networks, meaning that the same principles remain over time too. Our models allow us to produce full up-and-down self-similar multiscale replicas of complex networks that covers both large and small scales.

NETS2MAPS - Mercator is a new embedding tool to create maps of networks in the hyperbolic plane. Download it now from GitHub! Mercator is a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The algorithm mixes machine learning and maximum likelihood approaches to infer the coordinates of the nodes in the underlying hyperbolic disk with the best matching between the observed network topology and the geometric model. Overall, our results suggest that mixing machine learning and maximum likelihood techniques in a model-dependent framework can boost the meaningful mapping of complex networks.

Applications are invited for a Postdoctoral fellowship at the University of Barcelona to work with Prof. M. Ángeles Serrano and Prof. Marián Boguñá at the Department of Condensed Matter Physics and UB Institute of Complex Systems (UBICS). The position is funded by a Fundación BBVA grant.