Apparent Clustering and Apparent Background Earthquakes Biased by Undetected Seismicity

In models of triggered seismicity and in their inversion with empirical data, the detection threshold m_d is commonly equated to the magnitude m_0 of the smallest triggering earthquake. This unjustified assumption neglects the possibility of shocks below the detection threshold triggering observable events. We introduce a formalism that distinguishes between the detection threshold m_d and the minimum triggering earthquake m_0 < m_d. By considering the branching structure of one complete cascade of triggered events, we derive the apparent branching ratio n_a (which is the apparent fraction of aftershocks in a given catalog) and the apparent background source S_a that are observed when only the structure above the detection threshold m_d is known due to the presence of smaller undetected events that are capable of triggering larger events. If earthquake triggering is controlled in large part by the smallest magnitudes as several recent analyses have shown, this implies that previous estimates of the clustering parameters may significantly underestimate the true values: for instance, an observed fraction of 55% of aftershocks is renormalized into a true value of 75% of triggered events.Comment: 12 pages; incl. 6 Figures, AGU styl

Prefrontal Activity Links Nonoverlapping Events in Memory

The medial prefrontal cortex (mPFC) plays an important role in memory. By maintaining a working memory buffer, neurons in prelimbic (PL) mPFC may selectively contribute to learning associations between stimuli that are separated in time, as in trace fear conditioning (TFC). Until now, evidence for this bridging role was largely descriptive. Here we used optogenetics to silence neurons in the PL mPFC of rats during learning in TFC. Memory formation was prevented when mPFC was silenced specifically during the interval separating the cue and shock. Our results provide support for a working memory function for these cells and indicate that associating two noncontiguous stimuli requires bridging activity in PL mPFC

NR2A- and NR2B-containing NMDA Receptors in the Prelimbic Medial Prefrontal Cortex Differentially Mediate Trace, Delay, and Contextual Fear Conditioning

Activation of N-methyl-D-aspartate receptors (NMDAR) in the prelimbic medial prefrontal cortex (PL mPFC) is necessary for the acquisition of both trace and contextual fear memories, but it is not known how specific NR2 subunits support each association. The NR2B subunit confers unique properties to the NMDAR and may differentially regulate these two fear memories. Here we show that NR2A-containing NMDARs mediate trace, delay, and contextual fear memories, but NR2B-containing NMDARs are required only for trace conditioning, consistent with a role for PL mPFC in working memory

Adaptively Smoothed Seismicity Earthquake Forecasts for Italy

We present a model for estimating the probabilities of future earthquakes of magnitudes m > 4.95 in Italy. The model, a slightly modified version of the one proposed for California by Helmstetter et al. (2007) and Werner et al. (2010), approximates seismicity by a spatially heterogeneous, temporally homogeneous Poisson point process. The temporal, spatial and magnitude dimensions are entirely decoupled. Magnitudes are independently and identically distributed according to a tapered Gutenberg-Richter magnitude distribution. We estimated the spatial distribution of future seismicity by smoothing the locations of past earthquakes listed in two Italian catalogs: a short instrumental catalog and a longer instrumental and historical catalog. The bandwidth of the adaptive spatial kernel is estimated by optimizing the predictive power of the kernel estimate of the spatial earthquake density in retrospective forecasts. When available and trustworthy, we used small earthquakes m>2.95 to illuminate active fault structures and likely future epicenters. By calibrating the model on two catalogs of different duration to create two forecasts, we intend to quantify the loss (or gain) of predictability incurred when only a short but recent data record is available. Both forecasts, scaled to five and ten years, were submitted to the Italian prospective forecasting experiment of the global Collaboratory for the Study of Earthquake Predictability (CSEP). An earlier forecast from the model was submitted by Helmstetter et al. (2007) to the Regional Earthquake Likelihood Model (RELM) experiment in California, and, with over half of the five-year experiment over, the forecast performs better than its competitors.Comment: revised manuscript. 22 pages, 3 figures, 2 table

Grobner Bases for Finite-temperature Quantum Computing and their Complexity

Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated with homotopy in dimensions d <= 2 form a faithful representation of the fundamental group of a quantum system. We then show how the most general polynomial ring obtained for a fermionic quantum system does not, in fact, admit a faithful representation, and so give a general prescription for calcluating Grobner bases for finite temperature many-body quantum system and show that their complexity class is BQP

Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes

We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which past activity triggers future activity. The term "multivariate" refers to the property that events come in different types, with possibly different intra- and inter-triggering abilities. We develop the general formalism of the multivariate generating moment function for the cumulative number of first-generation and of all generation events triggered by a given mother event (the "shock") as a function of the current time $t$. This corresponds to studying the response function of the process. A variety of different systems have been analyzed. In particular, for systems in which triggering between events of different types proceeds through a one-dimension directed or symmetric chain of influence in type space, we report a novel hierarchy of intermediate asymptotic power law decays $\sim 1/t^{1-(m+1)\theta}$ of the rate of triggered events as a function of the distance $m$ of the events to the initial shock in the type space, where $0 < \theta <1$ for the relevant long-memory processes characterizing many natural and social systems. The richness of the generated time dynamics comes from the cascades of intermediate events of possibly different kinds, unfolding via a kind of inter-breeding genealogy.Comment: 40 pages, 8 figure

Bath's law Derived from the Gutenberg-Richter law and from Aftershock Properties

The empirical Bath's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we show that the origin of Bath's law is to be found in the selection procedure used to define mainshocks and aftershocks rather than in any difference in the mechanisms controlling the magnitude of the mainshock and of the aftershocks. We use the ETAS model of seismicity, which provides a more realistic model of aftershocks, based on (i) a universal Gutenberg-Richter (GR) law for all earthquakes, and on (ii) the increase of the number of aftershocks with the mainshock magnitude. Using numerical simulations of the ETAS model, we show that this model is in good agreement with Bath's law in a certain range of the model parameters.Comment: major revisions, in press in Geophys. Res. Let