Power Law Behavior and Self-Similarity in Modern Industrial Accidents

Self-Similarity and Power Laws

Power law behavior in designed and natural complex systems: self-organized criticality versus highly optimized tolerance

Power law scalings are abundant in natural and man-made complex systems, but the presence of a power law in itself is insufficient to specify the mechanism that generates it. It would be particularly valuable to understand the origin of the power law distribution of electrical blackout size versus frequency in national high-voltage power grids, in order to better moderate blackouts. The concept...

Long-time behavior and relaxation of power-law correlation in one-dimensional self-gravitating system

Long-time behavior of spatial power-law correlation in one-dimensional self-gravitating system is numerically investigated. It is found that the power-law structure persists even after the system is virialized. The structure gradually disappears owing to energy exchange among particles. Energy distribution is quasi-stationary after the system is virialized.

Indian Buffet Processes with Power-law Behavior

The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a three-parameter generalization of the IBP exhibiting power-law behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the stable-beta process and deriving the IBP corresponding to it. We find in...

Power-law behavior and condensation phenomena in disordered urn models

We investigate equilibrium statistical properties of a disordered urn model. New types of urn models are proposed, in which quenched disorder parameters play an important role in generating power-law behavior. We evaluate the occupation probability P (k) with which an urn has k balls by using the concept of statistical physics of disordered systems. In our new disordered urn model, we find that...