11,358 research outputs found
Critical Phenomena in Head-on Collisions of Neutron Stars
We found type I critical collapses of compact objects modeled by a polytropic
equation of state (EOS) with polytropic index without the
ultra-relativistic assumption. The object is formed in head-on collisions of
neutron stars. Further we showed that the critical collapse can occur due to a
change of the EOS, without fine tuning of initial data. This opens the
possibility that a neutron star like compact object, not just those formed in a
collision, may undergo a critical collapse in processes which slowly change the
EOS, such as cooling.Comment: 4 pages,6 figures, 15 reference
Covariate assisted screening and estimation
Consider a linear model , where and .
The vector is unknown but is sparse in the sense that most of its
coordinates are . The main interest is to separate its nonzero coordinates
from the zero ones (i.e., variable selection). Motivated by examples in
long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and
Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya
[In Change-Point Problems (South Hadley, MA, 1992) (1994) 28-56 IMS]), we are
primarily interested in the case where the Gram matrix is nonsparse but
sparsifiable by a finite order linear filter. We focus on the regime where
signals are both rare and weak so that successful variable selection is very
challenging but is still possible. We approach this problem by a new procedure
called the covariate assisted screening and estimation (CASE). CASE first uses
a linear filtering to reduce the original setting to a new regression model
where the corresponding Gram (covariance) matrix is sparse. The new covariance
matrix induces a sparse graph, which guides us to conduct multivariate
screening without visiting all the submodels. By interacting with the signal
sparsity, the graph enables us to decompose the original problem into many
separated small-size subproblems (if only we know where they are!). Linear
filtering also induces a so-called problem of information leakage, which can be
overcome by the newly introduced patching technique. Together, these give rise
to CASE, which is a two-stage screen and clean [Fan and Song Ann. Statist. 38
(2010) 3567-3604; Wasserman and Roeder Ann. Statist. 37 (2009) 2178-2201]
procedure, where we first identify candidates of these submodels by patching
and screening, and then re-examine each candidate to remove false positives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1243 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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