arXiv subjects

Hugo P. Maia

Publications and source records attributed to Hugo P. Maia.

4 recordsLinked to original sources

arXiv2026

Nesting Controls Phase Transitions in Higher-Order Contagion

The organization of higher-order interactions plays a central role in shaping collective dynamics, yet a general structural principle governing contagion on hypergraphs remains lacking. Here we introduce a nesting coefficient that quantifies how lower-order interactions are embedded within higher-order ones, defining a continuum between simplicial complexes and random hypergraphs. Using a higher-order susceptible-infected-susceptible model, we show that increasing nesting lowers the activation threshold and suppresses discontinuous transitions, while weak embedding favors explosive behavior. We further demonstrate that correlations between nesting and interaction order modulate the onset of activity while only weakly affecting transition discontinuity. Analysis of synthetic and empirical networks reveals that nesting strongly predicts hysteresis, establishing it as a key structural determinant of phase transitions in higher-order systems.

physics.soc-ph↗

arXiv2025

Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks

Higher-order interactions, where groups of nodes interact collectively rather than pairwisely, are central to many complex systems, from neural and ecological networks to social contagion. However, simulating dynamical processes on such higher-order structures remains computationally challenging due to the combinatorial growth of possible interactions. Here, we develop efficient and statistically exact Gillespie algorithms for Markovian spreading dynamics on large and heterogeneous hypergraphs. By incorporating phantom processes $-$events that advance time without altering the system's state$-$, we drastically reduce the computational complexity of standard algorithms ($\mathcal{O}(N^2)$), achieving up to linear scaling with system size. Relying on the susceptible-infected-susceptible model with critical mass thresholds as a benchmark, we show that the optimized algorithms outperform standard approaches by several orders of magnitude, enabling simulations of networks with millions of nodes and broad heterogeneity in both degree and interaction order. Efficient sampling methods, needed to overcome the bottlenecks imposed by either a high maximum order or number of interactions, and other dynamical processes on higher-order networks are tackled. These results establish a general framework for scalable, continuous-time simulations of higher-order contagion and related dynamical processes.

physics.soc-ph↗

arXiv2022

Controversy-seeking fuels rumor-telling activity in polarized opinion networks

Rumors have ignited revolutions, undermined the trust in political parties, or threatened the stability of human societies. Such destructive potential has been significantly enhanced by the development of on-line social networks. Several theoretical and computational studies have been devoted to understanding the dynamics and to control rumor spreading. In the present work, a model of rumor-telling in opinion polarized networks was investigated through extensive computer simulations. The key mechanism is the coupling between ones' opinions and their leaning to spread a given information, either by supporting or opposing its content. We report that a highly modular topology of polarized networks strongly impairs rumor spreading, but the couplings between agent's opinions and their spreading/stifling rates can either further inhibit or, conversely, foster information propagation, depending on the nature of those couplings. In particular, a controversy-seeking mechanism, in which agents are stimulated to postpone their transitions to the stiffer state upon interactions with other agents of confronting opinions, enhances the rumor spreading. Therefore such a mechanism is capable of overcoming the propagation bottlenecks imposed by loosely connected modular structures.

physics.soc-ph↗

arXiv2020

Adaptive network approach for emergence of societal bubbles

Far beyond its relevance for commercial and political marketings, opinion formation and decision making processes are central for representative democracy, government functioning, and state organization. In the present report, a stochastic agent-based model is investigated. The model assumes that bounded confidence and homophily mechanisms drive both opinion dynamics and social network evolution through either rewiring or breakage of social contacts. In addition to the classical transition from global consensus to opinion polarization, our main findings are (i) a cascade of fragmentation of the social network into echo chambers (modules) holding distinct opinions and rupture of the bridges interconnecting these modules as the tolerance for opinion differences increases. There are multiple surviving opinions associated to these modules within which consensus is formed; and (ii) the adaptive social network exhibits a hysteresis-like behavior characterized by irreversible changes in its topology as the opinion tolerance cycles from radicalization towards consensus and backward to radicalization.

physics.soc-ph↗