279 research outputs found
On the positive eigenvalues and eigenvectors of a non-negative matrix
The paper develops the general theory for the items in the title, assuming
that the matrix is countable and cofinal.Comment: Version 2 allows the matrix to have zero row(s) and rows with
infinitely many non-zero entries. In addition the introduction has been
rewritte
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
On the influence of time and space correlations on the next earthquake magnitude
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 of magnitude correlations. The standard approach generally assumes
that magnitudes are independent and therefore in principle unpredictable. Here
we show the existence of clustering in magnitude: earthquakes occur with higher
probability close in time, space and magnitude to previous events. More
precisely, the next earthquake tends to have a magnitude similar but smaller
than the previous one. A dynamical scaling relation between magnitude, time and
space distances reproduces the complex pattern of magnitude, spatial and
temporal correlations observed in experimental seismic catalogs.Comment: 4 Figure
A model for the distribution of aftershock waiting times
In this work the distribution of inter-occurrence times between earthquakes
in aftershock sequences is analyzed and a model based on a non-homogeneous
Poisson (NHP) process is proposed to quantify the observed scaling. In this
model the generalized Omori's law for the decay of aftershocks is used as a
time-dependent rate in the NHP process. The analytically derived distribution
of inter-occurrence times is applied to several major aftershock sequences in
California to confirm the validity of the proposed hypothesis.Comment: 4 pages, 3 figure
General moments of the inverse real Wishart distribution and orthogonal Weingarten functions
Let be a random positive definite symmetric matrix distributed according
to a real Wishart distribution and let be its inverse
matrix. We compute general moments explicitly. To do so, we employ the orthogonal Weingarten
function, which was recently introduced in the study for Haar-distributed
orthogonal matrices. As applications, we give formulas for moments of traces of
a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it
includes Appendi
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
Survival of branching random walks in random environment
We study survival of nearest-neighbour branching random walks in random
environment (BRWRE) on . A priori there are three different
regimes of survival: global survival, local survival, and strong local
survival. We show that local and strong local survival regimes coincide for
BRWRE and that they can be characterized with the spectral radius of the first
moment matrix of the process. These results are generalizations of the
classification of BRWRE in recurrent and transient regimes. Our main result is
a characterization of global survival that is given in terms of Lyapunov
exponents of an infinite product of i.i.d. random matrices.Comment: 17 pages; to appear in Journal of Theoretical Probabilit
Towards Landslide Predictions: Two Case Studies
In a previous work [Helmstetter, 2003], we have proposed a simple physical
model to explain the accelerating displacements preceding some catastrophic
landslides, based on a slider-block model with a state and velocity dependent
friction law. This model predicts two regimes of sliding, stable and unstable
leading to a critical finite-time singularity. This model was calibrated
quantitatively to the displacement and velocity data preceding two landslides,
Vaiont (Italian Alps) and La Clapi\`ere (French Alps), showing that the former
(resp. later) landslide is in the unstable (resp. stable) sliding regime. Here,
we test the predictive skills of the state-and-velocity-dependent model on
these two landslides, using a variety of techniques. For the Vaiont landslide,
our model provides good predictions of the critical time of failure up to 20
days before the collapse. Tests are also presented on the predictability of the
time of the change of regime for la Clapi\`ere landslide.Comment: 30 pages with 12 eps figure
Genetic factors predict hybrid formation in the British flora
Natural hybridization can have a profound evolutionary impact, with consequences ranging from the extinction of rare taxa to the origin of new species. Natural hybridization is particularly common in plants; however, our understanding of the general factors that promote or prevent hybridization is hampered by the highly variable outcomes in different lineages. Here, we quantify the influence of different predictors on hybrid formation across species from an entire flora. We combine estimates of hybridization with ecological attributes and a new species-level phylogeny for over 1,100 UK flowering plant species. Our results show that genetic factors, particularly parental genetic distance, as well as phylogenetic position and ploidy, are key determinants of hybrid formation, whereas many other factors such as range overlap and genus size explain much less variation in hybrid formation. Overall, intrinsic genetic factors shape the evolutionary and ecological consequences of natural hybridization across species in a flora
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