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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


Scaling up real networks by geometric branching growth

Muhua Zheng, Guillermo Garc√≠a-P√©rez, Mari√°n Bogu√Ī√°, M. √Āngeles Serrano
Proceedings of the National Academy of Sciences USA 118 e2018994118 (2021)
theory of complex networks  |  network geometry

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Network Geometry

Mari√°n Bogu√Ī√°, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. √Āngeles Serrano
Nature Reviews Physics 3 114-135 (2021)
theory of complex networks  |  network geometry


Geometric renormalization unravels self-similarity of the multiscale human connectome

Muhua Zheng, Antoine Allard, Patric Hagmann, Yasser Alem√°n-G √≥meze, M. √Āngeles Serrano
Proceedings of the National Academy of Sciences USA 117 20244-20253 (2020)
systems biology  |  brain