The detection and characterization of self-organized criticality (SOC), in both real and
simulated data, has undergone many significant revisions over the past 25 years. The …

The following chapter provides an overview of the techniques used to understand Self-
Organised Criticality (SOC) by performing computer simulations. Those are of particular …

Extreme events can come either from point processes, when the size or energy of the events
is above a certain threshold, or from time series, when the intensity of a signal surpasses a …

The thresholding of time series of activity or intensity is frequently used to define and
differentiate events. This is either implicit, for example due to resolution limits, or explicit, in …

The behavior of granular media under quasistatic loading has recently been shown to attain
a stable evolution state corresponding to a manifold in the space of micromechanical …

We perform a high-accuracy moment analysis of the avalanche size, duration and area
distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional …

Understanding the causes and effects of spatial vegetation patterns is a fundamental
problem in ecology, especially because these can be used as early predictors of …

The role of correlations in self-organized critical (SOC) phenomena is investigated by
studying the Abelian Manna model (AMM) in two dimensions. Local correlations of the …

A set of discrete individual points located in an embedding continuum space can be seen as
percolating or non-percolating, depending on the radius of the discs/spheres associated …

We introduce a novel approach to study the critical behavior of equilibrium and
nonequilibrium systems, which is based on the concept of an instantaneous correlation …