350 research outputs found
Properties of Foreshocks and Aftershocks of the Non-Conservative SOC Olami-Feder-Christensen Model: Triggered or Critical Earthquakes?
Following Hergarten and Neugebauer [2002] who discovered aftershock and
foreshock sequences in the Olami-Feder-Christensen (OFC) discrete block-spring
earthquake model, we investigate to what degree the simple toppling mechanism
of this model is sufficient to account for the properties of earthquake
clustering in time and space. Our main finding is that synthetic catalogs
generated by the OFC model share practically all properties of real seismicity
at a qualitative level, with however significant quantitative differences. We
find that OFC catalogs can be in large part described by the concept of
triggered seismicity but the properties of foreshocks depend on the mainshock
magnitude, in qualitative agreement with the critical earthquake model and in
disagreement with simple models of triggered seismicity such as the Epidemic
Type Aftershock Sequence (ETAS) model [Ogata, 1988]. Many other features of OFC
catalogs can be reproduced with the ETAS model with a weaker clustering than
real seismicity, i.e. for a very small average number of triggered earthquakes
of first generation per mother-earthquake.Comment: revtex, 19 pages, 8 eps figure
Vere-Jones' Self-Similar Branching Model
Motivated by its potential application to earthquake statistics, we study the
exactly self-similar branching process introduced recently by Vere-Jones, which
extends the ETAS class of conditional branching point-processes of triggered
seismicity. One of the main ingredient of Vere-Jones' model is that the power
law distribution of magnitudes m' of daughters of first-generation of a mother
of magnitude m has two branches m'm with
exponent beta+d, where beta and d are two positive parameters. We predict that
the distribution of magnitudes of events triggered by a mother of magnitude
over all generations has also two branches m'm
with exponent beta+h, with h= d \sqrt{1-s}, where s is the fraction of
triggered events. This corresponds to a renormalization of the exponent d into
h by the hierarchy of successive generations of triggered events. The empirical
absence of such two-branched distributions implies, if this model is seriously
considered, that the earth is close to criticality (s close to 1) so that beta
- h \approx \beta + h \approx \beta. We also find that, for a significant part
of the parameter space, the distribution of magnitudes over a full catalog
summed over an average steady flow of spontaneous sources (immigrants)
reproduces the distribution of the spontaneous sources and is blind to the
exponents beta, d of the distribution of triggered events.Comment: 13 page + 3 eps figure
Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes
We present a new method of data clustering applied to earthquake catalogs,
with the goal of reconstructing the seismically active part of fault networks.
We first use an original method to separate clustered events from uncorrelated
seismicity using the distribution of volumes of tetrahedra defined by closest
neighbor events in the original and randomized seismic catalogs. The spatial
disorder of the complex geometry of fault networks is then taken into account
by defining faults as probabilistic anisotropic kernels, whose structures are
motivated by properties of discontinuous tectonic deformation and previous
empirical observations of the geometry of faults and of earthquake clusters at
many spatial and temporal scales. Combining this a priori knowledge with
information theoretical arguments, we propose the Gaussian mixture approach
implemented in an Expectation-Maximization (EM) procedure. A cross-validation
scheme is then used and allows the determination of the number of kernels that
should be used to provide an optimal data clustering of the catalog. This
three-steps approach is applied to a high quality relocated catalog of the
seismicity following the 1986 Mount Lewis () event in California and
reveals that events cluster along planar patches of about 2 km, i.e.
comparable to the size of the main event. The finite thickness of those
clusters (about 290 m) suggests that events do not occur on well-defined
euclidean fault core surfaces, but rather that the damage zone surrounding
faults may be seismically active at depth. Finally, we propose a connection
between our methodology and multi-scale spatial analysis, based on the
derivation of spatial fractal dimension of about 1.8 for the set of hypocenters
in the Mnt Lewis area, consistent with recent observations on relocated
catalogs
Regulation of Extinction-Related Plasticity by Opioid Receptors in the Ventrolateral Periaqueductal Gray Matter
Recent work has led to a better understanding of the neural mechanisms underlying the extinction of Pavlovian fear conditioning. Long-term synaptic changes in the medial prefrontal cortex (mPFC) are critical for extinction learning, but very little is currently known about how the mPFC and other brain areas interact during extinction. The current study examined the effect of drugs that impair the extinction of fear conditioning on the activation of the extracellular-related kinase/mitogen-activated protein kinase (ERK/MAPK) in brain regions that likely participate in the consolidation of extinction learning. Inhibitors of opioid and N-methyl-d-aspartic acid (NMDA) receptors were applied to the ventrolateral periaqueductal gray matter (vlPAG) and amygdala shortly before extinction training. Results from these experiments show that blocking opioid receptors in the vlPAG prevented the formation of extinction memory, whereas NMDA receptor blockade had no effect. Conversely, blocking NMDA receptors in the amygdala disrupted the formation of fear extinction memory, but opioid receptor blockade in the same brain area did not. Subsequent experiments tested the effect of these drug treatments on the activation of the ERK/MAPK signaling pathway in various brain regions following extinction training. Only opioid receptor blockade in the vlPAG disrupted ERK phosphorylation in the mPFC and amygdala. These data support the idea that opiodergic signaling derived from the vlPAG affects plasticity across the brain circuit responsible for the formation of extinction memory
Multifractal Scaling of Thermally-Activated Rupture Processes
We propose a ``multifractal stress activation'' model combining thermally
activated rupture and long memory stress relaxation, which predicts that
seismic decay rates after mainshocks follow the Omori law with
exponents linearly increasing with the magnitude of the mainshock and
the inverse temperature. We carefully test this prediction on earthquake
sequences in the Southern California Earthquake catalog: we find power law
relaxations of seismic sequences triggered by mainshocks with exponents
increasing with the mainshock magnitude by approximately for each
magnitude unit increase, from to ,
in good agreement with the prediction of the multifractal model.Comment: four pages and 2 figure
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 . 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 of the rate of triggered events as a function of the
distance of the events to the initial shock in the type space, where 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
Short-term memory in gene induction reveals the regulatory principle behind stochastic IL-4 expression
Combining experiments on primary T cells and mathematical modeling, we characterized the stochastic expression of the interleukin-4 cytokine gene in its physiologic context, showing that a two-step model of transcriptional regulation acting on chromatin rearrangement and RNA polymerase recruitment accounts for the level, kinetics, and population variability of expression.A rate-limiting step upstream of transcription initiation, but occurring at the level of an individual allele, controls whether the interleukin-4 gene is expressed during antigenic stimulation, suggesting that the observed stochasticity of expression is linked to the dynamics of chromatin rearrangement.The computational analysis predicts that the probability to re-express an interleukin-4 gene that has been expressed once is transiently increased. In support, we experimentally demonstrate a short-term memory for interleukin-4 expression at the predicted time scale of several days.The model provides a unifying framework that accounts for both graded and binary modes of gene regulation. Graded changes in expression level can be achieved by controlling transcription initiation, whereas binary regulation acts at the level of chromatin rearrangement and is targeted during the differentiation of T cells that specialize in interleukin-4 production
Scale free networks of earthquakes and aftershocks
We propose a new metric to quantify the correlation between any two
earthquakes. The metric consists of a product involving the time interval and
spatial distance between two events, as well as the magnitude of the first one.
According to this metric, events typically are strongly correlated to only one
or a few preceding ones. Thus a classification of events as foreshocks, main
shocks or aftershocks emerges automatically without imposing predefined
space-time windows. To construct a network, each earthquake receives an
incoming link from its most correlated predecessor. The number of aftershocks
for any event, identified by its outgoing links, is found to be scale free with
exponent . The original Omori law with emerges as a
robust feature of seismicity, holding up to years even for aftershock sequences
initiated by intermediate magnitude events. The measured fat-tailed
distribution of distances between earthquakes and their aftershocks suggests
that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte
On the Occurrence of Finite-Time-Singularities in Epidemic Models of Rupture, Earthquakes and Starquakes
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,
based solely on the most solidly documented stylized facts of seismicity
(clustering in space and in time and power law Gutenberg-Richter distribution
of earthquake energies). This theory accounts for the main observations (power
law acceleration and discrete scale invariant structure) of critical rupture of
heterogeneous materials, of the largest sequence of starquakes ever attributed
to a neutron star as well as of earthquake sequences.Comment: Revtex document of 4 pages including 1 eps figur
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