Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an oversimplification, for instance, in social interactions that frequently occur within groups. To overcome this limitation, here we study the dynamics of social contagion on hypergraphs. We develop an analytical framework and provide numerical results for arbitrary hypergraphs, which we also support with Monte Carlo simulations. Our analyses show that the model has a vast parameter space, with continuous and discontinuous transitions, bistability, and hysteresis. Phenomenologically, we also extend the concept of latent heat to social contexts, which might help understand oscillatory social behaviors. Our work unfolds the research line of higher-order models and the analytical treatment of hypergraphs, posing new questions for modeling dynamical processes on higher-order structures.
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Guilherme has been working in nonlinear dynamics and stochastic processes on top of complex networks and higher-order structures. More specifically, on epidemic/rumor spreading and social contagion processes in single and multilayer networks and hypergraphs. He has focused on the theoretical and numerical methods developed for this study, formally defining the dynamical process and then validating and extending the theoretical results using numerical experiments and Monte Carlo simulations. Throughout the researcher's past works, spreading processes (disease, rumor, and social contagion models) were distinguished according to the temporal assumptions and its inherent mathematical assumptions, i.e., by distinguishing continuous-time and the discrete-time cellular automata approaches. Each formalism was studied using the appropriate tools, including the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean-field approaches, for the continuous-time and discrete-time Markov chains for the cellular automata-like processes. Among other interests and using these formalisms, the researcher was concerned about the impact of heterogeneity in the dynamical parameters, which is essential for more realistic models. Despite dynamics, he has also worked with the structural characterization of single and multilayer networks, mainly through spectral theory.