Structure and Dynamics of Hypergraphs
Visiting Speaker
Past Talk
Guilherme Ferraz de Arruda
Postdoctoral Researcher, ISI Foundation, Turin, Italy
Tuesday
Mar 29, 2022
Watch video
Time TBA
12:00 pm
177 Huntington Ave
11th floor
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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 assumption is often an oversimplification, for instance, in social interactions that frequently occur within groups. To overcome this limitation, we use hypergraphs, which are mathematical objects that impose virtually no constraints regarding the sizes of the interactions. From a practical viewpoint, our initial motivation was social science's experimental studies on how committed minorities can overturn an established behavior. Despite that, our research questions generally focus on more fundamental aspects, such as the relationship between structure and dynamics when considering higher-order interactions and the constraints this kind of structure might impose. In this talk, we will discuss a straightforward generalization of contagion dynamics that account for a collection of groups modeled by critical-mass processes. We will show that our model has a rich and unexpected behavior beyond discontinuous transitions. In particular, we might have multistability and intermittency due to bimodal state distributions. We will also comment on other processes such as random walks, cascading failure, and failures and attacks to relate them to higher-order systems' structural aspects. We hope that our works can have applications advancing our understanding of real higher-order systems and that our theory might be helpful in applications such as hypergraph neural networks and convolutional networks on hypergraphs.

About the speaker
About the speaker
Guilherme Ferraz de Arruda holds a Ph.D. in Computer Science and Computational Mathematics from ICMC - University of São Paulo (USP). Currently, he is a postdoctoral researcher at ISI Foundation. He 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, validating them, and extending the theoretical results using numerical experiments and Monte Carlo simulations. Throughout the his past works, spreading processes (disease, rumor, and social contagion models) were distinguished according to their temporal assumptions and their inherent mathematical assumptions, i.e., by distinguishing continuous-time and the discrete-time cellular automata approach. 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, Guilherme was concerned about the impact of heterogeneity in the dynamical parameters, which is essential for more realistic models. Despite studying dynamical processes, he has also worked with the structural characterization of networks and hypergraphs, mainly through spectral theory. For details, visit https://guifarruda.gitlab.io.
Guilherme Ferraz de Arruda holds a Ph.D. in Computer Science and Computational Mathematics from ICMC - University of São Paulo (USP). Currently, he is a postdoctoral researcher at ISI Foundation. He 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, validating them, and extending the theoretical results using numerical experiments and Monte Carlo simulations. Throughout the his past works, spreading processes (disease, rumor, and social contagion models) were distinguished according to their temporal assumptions and their inherent mathematical assumptions, i.e., by distinguishing continuous-time and the discrete-time cellular automata approach. 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, Guilherme was concerned about the impact of heterogeneity in the dynamical parameters, which is essential for more realistic models. Despite studying dynamical processes, he has also worked with the structural characterization of networks and hypergraphs, mainly through spectral theory. For details, visit https://guifarruda.gitlab.io.

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