12,823 research outputs found
A Statistical Perspective on Algorithmic Leveraging
One popular method for dealing with large-scale data sets is sampling. For
example, by using the empirical statistical leverage scores as an importance
sampling distribution, the method of algorithmic leveraging samples and
rescales rows/columns of data matrices to reduce the data size before
performing computations on the subproblem. This method has been successful in
improving computational efficiency of algorithms for matrix problems such as
least-squares approximation, least absolute deviations approximation, and
low-rank matrix approximation. Existing work has focused on algorithmic issues
such as worst-case running times and numerical issues associated with providing
high-quality implementations, but none of it addresses statistical aspects of
this method.
In this paper, we provide a simple yet effective framework to evaluate the
statistical properties of algorithmic leveraging in the context of estimating
parameters in a linear regression model with a fixed number of predictors. We
show that from the statistical perspective of bias and variance, neither
leverage-based sampling nor uniform sampling dominates the other. This result
is particularly striking, given the well-known result that, from the
algorithmic perspective of worst-case analysis, leverage-based sampling
provides uniformly superior worst-case algorithmic results, when compared with
uniform sampling. Based on these theoretical results, we propose and analyze
two new leveraging algorithms. A detailed empirical evaluation of existing
leverage-based methods as well as these two new methods is carried out on both
synthetic and real data sets. The empirical results indicate that our theory is
a good predictor of practical performance of existing and new leverage-based
algorithms and that the new algorithms achieve improved performance.Comment: 44 pages, 17 figure
HEN1 recognizes 21-24 nt small RNA duplexes and deposits a methyl group onto the 2' OH of the 3' terminal nucleotide.
microRNAs (miRNAs) and small interfering RNAs (siRNAs) in plants bear a methyl group on the ribose of the 3' terminal nucleotide. We showed previously that the methylation of miRNAs and siRNAs requires the protein HEN1 in vivo and that purified HEN1 protein methylates miRNA/miRNA* duplexes in vitro. In this study, we show that HEN1 methylates both miRNA/miRNA* and siRNA/siRNA* duplexes in vitro with a preference for 21-24 nt RNA duplexes with 2 nt overhangs. We also demonstrate that HEN1 deposits the methyl group on to the 2' OH of the 3' terminal nucleotide. Among various modifications that can occur on the ribose of the terminal nucleotide, such as 2'-deoxy, 3'-deoxy, 2'-O-methyl and 3'-O-methyl, only 2'-O-methyl on a small RNA inhibits the activity of yeast poly(A) polymerase (PAP). These findings indicate that HEN1 specifically methylates miRNAs and siRNAs and implicate the importance of the 2'-O-methyl group in the biology of RNA silencing
Quasinormal modes and late-time tails in the background of Schwarzschild black hole pierced by a cosmic string: scalar, electromagnetic and gravitational perturbations
We have studied the quasinormal modes and the late-time tail behaviors of
scalar, electromagnetic and gravitational perturbations in the Schwarzschild
black hole pierced by a cosmic string. Although the metric is locally identical
to that of the Schwarzschild black hole so that the presence of the string will
not imprint in the motion of test particles, we found that quasinormal modes
and the late-time tails can reflect physical signatures of the cosmic string.
Compared with the scalar and electromagnetic fields, the gravitational
perturbation decays slower, which could be more interesting to disclose the
string effect in this background.Comment: 17 pages; 7 figure
Toward parton equilibration with improved parton interaction matrix elements
The Quark-Gluon Plasma can be produced in high energy heavy ion collisions
and how it equilibrates is important for the extraction of the properties of
strongly interacting matter. A radiative transport model can be used to reveal
interesting characteristics of Quark-Gluon Plasma thermalization. For example,
screened parton interactions always lead to partial pressure isotropization.
Systems with different initial pressure anisotropies evolve toward the same
asymptotic evolution. In particular, radiative processes are crucial for the
chemical equilibration of the system. Matrix elements under the soft and
collinear approximation for these processes, as first derived by Gunion and
Bertsch, are widely used. A different approach is to start with the exact
matrix elements for the two to three and its inverse processes. General
features of this approach will be reviewed and the results will be compared
with the Gunion-Bertsch results. We will comment on the possible implications
of the exact matrix element approach on Quark-Gluon Plasma thermalization.Comment: Presented at the 11th International Conference on Nucleus-Nucleus
Collisions (NN2012), San Antonio, Texas, USA, 27 May-1 June 201
Evolution of cooperation in multilevel public goods games with community structures
In a community-structured population, public goods games (PGG) occur both
within and between communities. Such type of PGG is referred as multilevel
public goods games (MPGG). We propose a minimalist evolutionary model of the
MPGG and analytically study the evolution of cooperation. We demonstrate that
in the case of sufficiently large community size and community number, if the
imitation strength within community is weak, i.e., an individual imitates
another one in the same community almost randomly, cooperation as well as
punishment are more abundant than defection in the long run; if the imitation
strength between communities is strong, i.e., the more successful strategy in
two individuals from distinct communities is always imitated, cooperation and
punishment are also more abundant. However, when both of the two imitation
intensities are strong, defection becomes the most abundant strategy in the
population. Our model provides insight into the investigation of the
large-scale cooperation in public social dilemma among contemporary
communities.Comment: 6 pages, 4 figures, Accepted by EP
Chemical and kinetic equilibrations via radiative parton transport
A hot and dense partonic system can be produced in the early stage of a
relativistic heavy ion collision. How it equilibrates is important for the
extraction of Quark-Gluon Plasma properties. We study the chemical and kinetic
equilibrations of the Quark-Gluon Plasma using a radiative transport model.
Thermal and Color-Glass-Condensate motivated initial conditions are used. We
observe that screened parton interactions always lead to partial pressure
isotropization. Different initial pressure anisotropies result in the same
asymptotic evolution. Comparison of evolutions with and without radiative
processes shows that chemical equilibration interacts with kinetic
equilibration and radiative processes can contribute significantly to pressure
isotropization.Comment: Presented at 24th International Nuclear Physics Conference
(INPC2010), Vancouver, Canada, 4-9 July 201
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