In the last two decades, networks provided a successful theoretical and computational framework to model, analyze and predict structure and dynamics of complex interconnected systems. However, many empirical systems consist of units which exhibit different types of physical or functional relationships. Emblematic examples are the nervous systems (e.g., neurons can interact chemically or electrically), molecular systems (e.g., gene-protein interactions can be additive, suppressive, etc), social systems (e.g., family, business and trust relationships) or transportation systems (e.g., road, rail and flight networks of cities).
Multilayer networks have been introduced to account for this crucial feature of real systems. In this talk we will briefly introduce their mathematical formulation [1], a key ingredient to define random walk dynamics in these systems [2,3]. We will mention the identification of key units [4], their mesoscale organization [5] and the overall resilience to perturbations [6] by reviewing some successful applications to human brain [7], social [4,6] and molecular systems [8].
[1] MDD et al, Phys. Rev. X 3, 041022 (2013)
[2] MDD, A. Sole-Ribalta, S. Gomez, A. Arenas, PNAS 11, 8351 (2014)
[3] MDD, C. Granell, M.A. Porter, A. Arenas, Nature Physics 12, 901 (2016)
[4] MDD, A. Sole-Ribalta, E. Omodei, S. Gomez, A. Arenas, Nature Communications 6, 6868 (2015)
[5] MDD, A. Lancichinetti, A. Arenas, M. Rosvall, Physical Review X 5, 011027 (2015)
[6] J.A. Baggio, S.B. BurnSilver, A. Arenas, J.S. Magdanzd, G.P. Kofinasd, MDD, PNAS 113, 13708 (2016)
[7] MDD, S. Sasai, A. Arenas, Frontiers in Neuroscience 10, 326 (2016)
[8] MDD, V. Nicosia, A. Arenas, V. Latora, Nature Communications 6, 6864 (2015)
Agenda
