Triadic Approximation Reveals the Role of Interaction Overlap on the Spread of Complex Contagions on Higher-Order Networks.

Contagion processes relying on the exposure to multiple sources are prevalent in social systems, and are effectively represented by hypergraphs. In this Letter, we derive a mean-field model that goes beyond node- and pair-based approximations. We reveal how the stability of the contagion-free state is decided by either two- or three-body interactions, and how this is strictly related to the degree of overlap between these interactions. Our findings demonstrate the dual effect of increased overlap: it lowers the invasion threshold, yet produces smaller outbreaks. Corroborated by numerical simulations, our results emphasize the significance of the chosen representation in describing a higher-order process.

Spreading dynamics in networks under context-dependent behavior.

In some systems, the behavior of the constituent units can create a "context" that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading. In our model, agents actively impede (favor) or not diffusion during an interaction, depending on the behavior they observe among all the peers in the group within which that interaction occurs. We divide the population into two behavioral types and provide a mean-field theory to parametrize mixing patterns of arbitrary type-assortativity within groups of any size. As an application, we examine an epidemic-spreading model with context-dependent adoption of prophylactic tools such as face masks. By analyzing the distributions of groups' size and type-composition, we uncover a rich phenomenology for the basic reproduction number and the endemic state. We analytically show how changing the group organization of contacts can either facilitate or hinder epidemic spreading, eventually moving the system from the subcritical to the supercritical phase and vice versa, depending mainly on sociological factors, such as whether the prophylactic behavior is hardly or easily induced. More generally, our work provides a theoretical foundation to model higher-order contexts and analyze their dynamical implications, envisioning a broad theory of context-dependent interactions that would allow for a new systematic investigation of a variety of complex systems.

Evolution of Cooperation in the Presence of Higher-Order Interactions: From Networks to Hypergraphs.

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise to network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.

Exploring the role of interdisciplinarity in physics: Success, talent and luck.

Although interdisciplinarity is often touted as a necessity for modern research, the evidence on the relative impact of sectorial versus to interdisciplinary science is qualitative at best. In this paper we leverage the bibliographic data set of the American Physical Society to quantify the role of interdisciplinarity in physics, and that of talent and luck in achieving success in scientific careers. We analyze a period of 30 years (1980-2009) tagging papers and their authors by means of the Physics and Astronomy Classification Scheme (PACS), to show that some degree of interdisciplinarity is quite helpful to reach success, measured as a proxy of either the number of articles or the citations score. We also propose an agent-based model of the publication-reputation-citation dynamics which reproduces the trends observed in the APS data set. On the one hand, the results highlight the crucial role of randomness and serendipity in real scientific research; on the other, they shed light on a counterintuitive effect indicating that the most talented authors are not necessarily the most successful ones.