Related papers: Predictability in the ETAS Model of Interacting Tr…
Event-triggered control (ETC) is claimed to provide enormous reductions in sampling frequency when compared to periodic sampling, but little is formally known about its generated traffic. This work shows that ETC can exhibit very complex,…
The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been…
The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event.…
The Multifractal Stress-Activated (MSA) model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of the Omori law…
The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used…
The Hawkes process is a versatile stochastic model for point patterns that exhibit self-excitation, that is, the property that an event occurrence increases the rate of occurrence for some period of time in the future. We present a Bayesian…
The decay rate of aftershocks is commonly very well described by the modified Omori law, $n(t) \propto t^{-p}$, where n(t) is the number of aftershocks per unit time, t is the time after the main shock, and p is a constant in the range…
For decades, classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes. Recent advances have led to Neural Point Processes…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number…
We have developed a model that describes the major characteristics of a rupture, ranging from regular earthquakes (EQs) to slow slip events (SSEs), including episodic tremor and slip (ETS). Previous model predictions, while accurate, are…
Earthquake aftershock identification is closely related to the question "Are aftershocks different from the rest of earthquakes?" We give a positive answer to this question and introduce a general statistical procedure for clustering…
We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…
The efficient exchange of information is an essential aspect of intelligent collective behavior. Event-triggered control and estimation achieve some efficiency by replacing continuous data exchange between agents with intermittent, or…
The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ~ 1/(t_c-t)^p' of the time to the mainshock occurring at t_c. Here, we show that this…
The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay…
Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade…
Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…