Related papers: Criticality in spreading processes without time-sc…
Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for…
It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…
We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the…
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the…
Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold…
Connectivity patterns of relevance in neuroscience and systems biology can be encoded in hierarchical modular networks (HMNs). Moreover, recent studies highlight the role of hierarchical modular organization in shaping brain activity…
With the advancement of computational network science, its research scope has significantly expanded beyond static graphs to encompass more complex structures. The introduction of streaming, temporal, multilayer, and hypernetwork approaches…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Many studies have found evidence that the brain operates at a critical point, a processus known as self-organized criticality. A recent paper found remarkable scalings suggestive of criticality in systems as different as neural cultures,…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model…
The hierarchical organization of the brain is a fundamental structural principle, while brain criticality is a leading hypothesis for its collective dynamics. However, the connection between structure and signatures of criticality remains…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…
We show that a simple model for the propagation of a rumor on a small-world network exhibits critical behavior at a finite randomness of the underlying graph. The transition occurs between a regime where the rumor "dies" in a small…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The critical brain hypothesis posits that neural systems operate near a phase transition, optimizing the processing of information. While scale invariance and non-Gaussian dynamics--hallmarks of criticality--have been observed in brain…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…