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Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted reaction–diffusion systems, voter or opinion formation models, etc.). Originated in the domain of theoretical and matter physics, it has many applications in epidemiology, sociology and, of course, computer and Internet sciences. In this review, we illustrate some aspects of percolation theory and its generalization, cellular automata and briefly discuss their relationship with equilibrium systems (Ising and Potts models). We present a model of opinion spreading, the role of the topology of the network to induce coherent oscillations and the influence (and advantages) of risk perception for stopping epidemics. The models and computational tools that are briefly presented here have an application to the filtering of tainted information in automatic trading. Finally, we introduce the open problem of controlling percolation and other processes on distributed systems.
Henry Markram, Felix Schürmann, Eilif Benjamin Muller, Srikanth Ramaswamy, Michael Reimann, Werner Alfons Hilda Van Geit, James Gonzalo King, Marwan Muhammad Ahmed Abdellah, Lida Kanari, Pramod Shivaji Kumbhar, Alexis Arnaudon, Ying Shi, Jean-Denis Georges Emile Courcol, Armando Romani, András Ecker, Michael Emiel Gevaert, Michele Migliore, Cyrille Pierre Henri Favreau, Vishal Sood, Cristina Colangelo, Mohameth François Sy, Judit Planas Carbonell, Szabolcs Kali, Genrich Ivaska, Carmen Alina Lupascu, Elvis Boci, Alberto Antonietti, Fabien Petitjean, Julian Martin Budd, Elisabetta Giacalone, Davide Bella, Mustafa Kerem Kurban, Pranav Rai, Juan Bautista Hernando Vieites, Huanxiang Lu, Liesbeth Maria L Vanherpe, Joni Henrikki Herttuainen, Rosanna Migliore, Anna-Kristin Kaufmann, Juan Luis Riquelme Roman, Sàra Sàray, Audrey Mercer, Thomas Brice Delemontex, Nadir Roman Guerrero