Global statistical tests for clustered earthquake pattern discovery in Italy

It is a widely shared opinion that not only secondary earthquakes (aftershocks) but also main earthquakes tend to occur in time-space clusters. The importance of this assumption requires the application of statistical tools to objectively evaluate its coherence with the reality at different scales of size-space-time. Global tests allow us to select the data sets with significant space-time clustering in order to perform more in-depth analyses to detect cluster locations. According to different fixed magnitude thresholds, we perform two global statistical tests, the Knox test and the Jacquez test, based on the space-time distance between pairs of earthquakes under the null hypothesis of uniform distribution in time and space, and evaluate the significance of the possible clusters. We analyze subsets of historical Italian earthquakes drawn from the Parametric Catalog of Italian Earthquakes (CPTI04) with magnitude thresholds 4.5, 5.3 and 6.0, associated with the composite seismogenic sources of the Database of Individual Seismogenic Sources. Each subset is related to one of the eight tectonically homogeneous macroregions in which the Italian territory has been divided. Significant space-time clustering is found for all sets with a magnitude threshold of 4.5. This tendency decreases drastically or disappears when the cut off rises to 5.3, with the exception of two macroregions located in the Eastern Alps and the Calabrian Arc, respectively, where evidence of space-time interaction may refer to stress transfer among consecutive or adjacent faults. The link between clustering effect and tectonic behavior could guide the choice of different stochastic point processes to model the seismic activity.

A fluid limit for a cache algorithm with general request processes

We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.