Fundamental Science for Society FS2

Mapping Complexity

By M. Ángeles Serrano and Marián Boguñá

Fundamental Science for Society FS2

Complex systems, such as societies, the Internet, the human brain, molecular networks within cells, international trade, and many others, are ubiquitous and around us. We are using networks to uncover the fundamental principles governing their structure, function, evolution, adaptability, and for modeling and predicting their behavior.

Foundation of Complex Networks

Networks are graph representations of complex real-world systems. In the network representation, the system's components are symbolized by vertices or nodes, while the interactions between these elements are depicted by edges or links organized into non-trivial connectivity patterns. The interplay between network structure and dynamic processes give rise to emergent behaviors, including phase transitions. We are deciphering the common language of complex networks.

Network Geometry

Geometry emerges as the most compelling rationale for the intricate structural patterns evident in real networks. Interestingly, the effective geometry of real networks is hyperbolic. The presence of a metric space governing network interactions provides a plausible explanation for the most fundamental topological attributes, including scale-free degree distributions, clustering, the small-world phenomenon, community structures, reciprocity, self-similarity, and many others.

Real Networks and Complex Data Structures

An intricate web of relationships across a wide range of spatiotemporal scales underpin various natural and human-made systems, and relational datasets. These networks can range from gene regulatory networks to social networks, international trade, and the Internet and other critical infrastructures. Their study unveils hidden patterns and emergent properties, enabling us to optimize their behavior and to reduce their vulnerability to cascades, crisis, catastrophes, and other critical and extreme events. In parallel, relational data structures are the lifeblood of decision-making, an understanding them is paramount for making informed choices in a diverse array of fields, from science and engineering to business and social policy.

Understanding Neural Networks

Neural networks, originally a model to simulate the intelligent behavior of the brain, are a fundamental component of modern artificial intelligence. Both natural and artificial neural networks comprise interconnected nodes that learn from data. Ramon y Cajal's discoveries ignited modern neuroscience. However, understanding the anatomical connectivity in the brain and how it is related with function and behavior remains a formidable challenge. Neural networks have reached a level of sophistication and versatility excelling in tasks like image recognition, natural language processing, and decision-making. Yet their functioning remains a black box. Opening the box may eventually help us to understand the functioning of natural brains.

Networks in Cosmology

The causal structure of spacetime and standard cosmological models readily aligns with hyperbolic geometry. Remarkably, networks that manifest within this framework exhibit striking similarities to networks encountered in a wide array of domains, ranging from cell biology and social sciences to complex socio-technological systems such as the Internet and the World Wide Web.
Highlights and Latest News

Read The Conversation article “Shake and divide: the cocktail formula for global consensus”

New paper in Nature Communications: The D-Mercator method for the multidimensional hyperbolic embedding of real networks

New paper in Nature Physics: Geometric description of clustering in directed networks

Ongoing Projects

We develop mathematical models and computational tools to investigate a wide variety of real complex systems, ranging from biological to economic and socio-technological systems. We characterize these systems using massive datasets.

Nets2Maps

The geometry of complexity

SD/HD+1 models · maps and embedding tools · navigability · multiscale · dimensionality · functional patterns

Networks at the Multiscale

Length scales and distances

renormalization · self-similarity · growth and evolution

Dynamics on and of Networks

The structure-function interplay

Turing patterns · epidemics · opinion formation · decision making · network evolution

Brain Networks

Multiscale features

connectomes · communication · navigability · multiscale

Networks in Cosmology

Discretizing spacetime

directed acyclic graphs · causal sets · Milne cosmology · de Sitter spacetime

Interpretability of Neural Networks

Opening the black box

graph neural networks · feature-enriched network geometry

People

Group Leaders

M. Ángeles Serrano,
ICREA Research Professor

Marián Boguñá,
Professor

Postdoctoral Researchers and PhD Students

Lucía Ramírez, PhD

Roya Aliakbarisani, PhD

Laia Barjuan

Robert Jankowski

Jasper van der Kolk

Master and Undergraduate Students

Meritxell Vila

Carla Caro

See the whole group

Contact

M. Ángeles Serrano
marian.serrano@ub.edu, +34934021153
Office 4.06

Marián Boguñá
marian.boguna@ub.edu, +34934039211
Office 4.16

Department of Condensed Matter Physics
Faculty of Physics, University of Barcelona

Martí i Franquès, 1 – 08028 Barcelona, Spain

University of Barcelona | UBICS | ICREA

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