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The hyperbolic brain

2020/10/01   |   academic

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.

Mercator

2019/12/05   |   academic

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.

Renormalizing complex networks

2019/03/20   |   academic

Maps of complex networks in hyperbolic space are not only attractive visual representations but they are full of meaning and allow us to find out information on the systems and to navigate through them. We can increase the system navigability if we take into account the information provided by the renormalization group, which allows us to unfold networks at the different structural scales that build them up, and which, in addition, turn out to be self-similar, that is, they have the same organization at different scales. These results can also be applied to make reduced versions of the original networks at smaller scales and which have the same properties. The possibility of having reduced copies has a great potential; for instance, they can serve as testbeds to assess expensive processes in original networks, such as new Internet routing protocols.





latest publications


Geometric renormalization unravels self-similarity of the multiscale human connectome

Muhua Zheng, Antoine Allard, Patric Hagmann, Yasser Alem√°n-G √≥meze, M. √Āngeles Serrano
PNAS 117 20244-20253 (2020)
systems biology  |  brain

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Geometric detection of hierarchical backbones in real networks

Elisenda Ortiz, Guillermo Garc√≠a-P√©rez, M. √Āngeles Serrano
Physical Review Research 2 033519 (2020)
theory of complex networks  |  network geometry


Precision as a measure of predictability of missing links in real networks

Guillermo Garc√≠a-P√©rez, Roya Aliakbarisani, Abdorasoul Ghasemi, M. √Āngeles Serrano
Physical Review E 101 052318 (2020)
theory of complex networks  |  link prediction