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An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e., the temporal profiles that characterize the growth and decay of avalanches of fixed duration. At the critical point of the dynamics the average avalanche shapes for different durations can be rescaled so that they collapse onto a single universal curve. We apply Markov branching process theory to derive a simple equation governing the average avalanche shape for cascade dynamics on networks. Analysis of the equation at criticality demonstrates that nonsymmetric average avalanche shapes (as observed in some experiments) occur for certain combinations of dynamics and network topology; specifically, on networks with heavy-tailed degree distributions. We give examples using numerical simulations of models for information spreading, neural dynamics, and behaviour adoption and we propose simple experimental tests to quantify whether cascading systems are in the critical state.
Based on a theoretical model for opinion spreading on a network, through avalanches, the effect of external field is now considered, by using methods from non-equilibrium statistical mechanics. The original part contains the implementation that the a
Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gather
Productive societies feature high levels of cooperation and strong connections between individuals. Public Goods Games (PGGs) are frequently used to study the development of social connections and cooperative behavior in model societies. In such game
Power-grid systems constitute one of the most complex man-made spatially extended structures. These operate with strict operational bounds to ensure synchrony across the grid. This is particularly relevant for power-grid frequency, which operates str
We study the effect of localized attacks on a multiplex spatial network, where each layer is a network of communities. The system is considered functional when the nodes belong to the giant component in all the multiplex layers. The communities are o