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South American Institute for Fundamental Research (ICTP-SAIFR)

Complex systems are characterized by a large number of units, such as particles, individuals or neurons, that interact typically with a few neighbors but lead to the emergence of large-scale collective behavior. Examples include swarms of birds, the spreading of infectious diseases, the transmission of electric impulses by neurons, and the synchronization of fireflies at nightfall. Networks provide a natural representation of these systems, where nodes play the role of the units, and links between nodes indicate pairwise interactions. The distribution of links among the nodes is a key property of networks, defining how the units of the system interact. Links may follow simple rules, such as regular lattices or random connections, or may be highly heterogeneous, displaying power law distributions. More recently, the concepts of multilayer and higher-order networks have emerged to describe interconnected sets of networks and many-body interactions, where single-layer networks are generalized to simplicial complexes or hypergraphs. Two of these processes have become particularly important and will be the focus of this workshop in terms of applications.