To account for the dissipative mechanisms found in nature, non-conservative elements have been incorporated in the energy redistribution rules of sandpiles and similar models of hazard phenomena. In this work, we found that incorporating non-conservation in the form of spatially-distributed sink sites affect both the external driving and internal cascade mechanisms of the sandpile. Increasing sink densities result in the loss of critical behavior, as evidenced by the gradual evolution of the avalanche size distribution from power-law (correlated) to exponential (random). For low density cases, we found no optimal configuration that will minimize the risk of producing large avalanches. Our model is inspired by analogs in natural avalanche systems, where non-conservative elements have an inherent spatial distribution.
Loss of criticality in the avalanche statistics of sandpiles with dissipative sites
Antonino A. Paguirigan Jr., Christopher P. Monterola, Rene C. Batac
Advanced inference techniques allow one to reconstruct a pattern of interaction from high dimensional data sets, from probing simultaneously thousands of units of extended systems?such as cells, neural tissues and financial markets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to singular values of parameters, akin to critical points in physics where phase transitions occur. These are points where the response of physical systems to external perturbations, as measured by the susceptibility, is very large and diverges in the limit of infinite size. We show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher information) are directly related to the susceptibility of the inferred model. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. This region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time scales naturally yield models which are close to criticality.
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