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It has been long stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallelisms between these so separate phenomena. We study the Acoustic…

A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence…

We study the change detection problem with an unknown post-change distribution. Under this constraint, the unknown change in the distribution of observations may occur in many ways without much structure on the observations, whereas, before…

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two…

The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate-and-state dependent friction law is studied by means of extensive computer simulations. It is found that…

Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability…

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum…

We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…

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 threshold value. We are particularly concerned by the…

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal…

Forecasting earthquake sequences remains a central challenge in seismology, particularly under non-stationary conditions. While deep learning models have shown promise, their ability to generalize across time remains poorly understood. We…

We study the asymptotic distribution for the occurrence time of the next large earthquake, by knowing the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is asymptotically…

Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…

Terra Seismic can predict most major earthquakes (M6.2 or greater) at least 2 - 5 months before they will strike. Global earthquake prediction is based on determinations of the stressed areas that will start to behave abnormally before…

The identification of patterns in space, time, and magnitude, which could potentially encode the subsequent earthquake magnitude, represents a significant challenge in earthquake forecasting. A pivotal aspect of this endeavor involves the…

We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strain release increases as a power-law…

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale…