Related papers: Criticality in spreading processes without time-sc…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question…
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…
Epidemic models are increasingly used in real-world networks to understand diffusion phenomena (such as the spread of diseases, emotions, innovations, failures) or the transport of information (such as news, memes in social on-line…
Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs…
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in…
Critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random walk problem. We obtain the analytic results for the critical scaling, using the event-driven dynamics approach. These results…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…
A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up "new ideas". Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas…
Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species…
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting…
We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos. Dropout shifts the perfect-alignment fixed point, making the depth scale for information propagation finite even at critical…
Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least $r$ active neighbors. Such process, originally studied on regular structures, has been recently investigated also in…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…