The VI AMMCS International Conference

Waterloo, Ontario, Canada | August 14-18, 2023

AMMCS 2023 Plenary Talk

Network geometry: from multiscale to ultra low dimensional representations of complex systems

M. Angeles Serrano (Universitat de Barcelona)

Recent advances in network science include the discovery that hyperbolic geometry captures the complex connectivity of real networks. Within this paradigm, we have been developing model-based methods for exploring their multiscale nature and their intrinsic dimensionality. More specifically, we produced a renormalization group technique that progressively coarse-grains and rescales networks, revealing a hierarchy of layers at different resolutions. We found that the multiscale shells of real networks, such as connectomes of the human brain, exhibit self-similarity across multiple scales. This symmetry is also evident in the growth of some real networks, suggesting that evolution can be modeled by a reverse renormalization process. In addition, geometric renormalization has practical applications, allowing us to produce scaled down and scaled up replicas of real networks. Our results were obtained by embedding real networks in two-dimensional hyperbolic space, but we have also developed a method to infer their intrinsic dimensionality since there is not fundamental reason to believe that it must be two. Our analysis has revealed ultra low dimensionality and unexpected regularities across different domains, such as extremely low dimensionality in tissue-specific biomolecular networks, close-to-three-dimensional brain connectomes, and slightly higher dimensionality in social networks and the Internet.
M. Angeles Serrano is an ICREA Research Professor at the Dept. of Condensed Matter Physics of the University of Barcelona (UB), where she leads the Mapping Complexity Lab. She also holds an appointment as an External Faculty at the Complexity Science Hub CSH in Vienna. A native of Barcelona, M.A.S. received a Ph.D. in theoretical physics from UB in 1999 and, a year later, a master in mathematics for finance from the Centre de Recerca Matematica CRM. She spent several years in the private sector and returned to academia in 2004 to work in network science. She conducted postdoctoral research at Indiana University (USA), the ecole Polytechnique Federale de Lausanne (Switzerland), and IFISC Institute (Spain), and was awarded a Ramon y Cajal Fellowship in 2009. M.A.S. has published in major peer reviewed international scientific journals including Nature Reviews Physics, Nature Physics, Nature Communications, PNAS, Phys Rev Letters, and more. She obtained the Outstanding Referee Award of the American Physical Society (APS) and a James McDonnell Foundation Scholar Award for the Study of Complex Systems.
She serves as a Board member of the Statistical and Nonlinear Physics Division of the European Physical Society, and belongs to the Editorial Board of the APS journal Physical Review Research. She is a founding member of Complexitat, the Catalan network for the study of complex systems, and a promoter and Scientific Board member of UBICS, the Universitat de Barcelona Institute of Complex Systems. M.A.S. is astonished by the amazing features that emerge in the structure, function, and evolution of complex systems, and she is using networks to model and to predict them.