35,007 research outputs found
Optimal Estimation of Slope Vector in High-dimensional Linear Transformation Model
In a linear transformation model, there exists an unknown monotone nonlinear
transformation function such that the transformed response variable and the
predictor variables satisfy a linear regression model. In this paper, we
present CENet, a new method for estimating the slope vector and simultaneously
performing variable selection in the high-dimensional sparse linear
transformation model. CENet is the solution to a convex optimization problem
and can be computed efficiently from an algorithm with guaranteed convergence
to the global optimum. We show that under a pairwise elliptical distribution
assumption on each predictor-transformed-response pair and some regularity
conditions, CENet attains the same optimal rate of convergence as the best
regression method in the high-dimensional sparse linear regression model. To
the best of our limited knowledge, this is the first such result in the
literature. We demonstrate the empirical performance of CENet on both simulated
and real datasets. We also discuss the connection of CENet with some nonlinear
regression/multivariate methods proposed in the literature.Comment: 25 pages, 7 figures, 1 tabl
A New Equation of State for Dark Energy Model
A new parameterization for the dark energy equation of state(EoS) is proposed
and some of its cosmological consequences are also investigated. This new
parameterization is the modification of Efstathiou' dark energy EoS
parameterization. is a well behaved function for and has same
behavior in at low redshifts with Efstathiou' parameterization. In this
parameterization there are two free parameter and . We discuss the
constraints on this model's parameters from current observational data. The
best fit values of the cosmological parameters with confidence-level
regions are: ,
and .Comment: 5 pages, 3 figures.some statement is change
Possible direct measurement of the expansion rate of the universe
A new method is proposed for directly measuring the expansion rate of the
universe through very precise measurement of the fluence of extremely stable
sources. The method is based on the definition of the luminosity distance and
its change along the time due to the cosmic expansion. It is argued that
galaxies may be chosen as the targets of the observation to perform the
measurement. We show that, by simultaneously increasing the observation time
and physically adding the fluences from different galaxies, the requirement on
the relative precision of the detector for an observation of 1 second on a
single galaxy can be relaxed to . Benefiting from the abundance of
galaxies in the universe, the method may be quite promising.Comment: 6 pages, 2 figures; added discussion about how to perform the
measuremen
Simple and Effective Dynamic Provisioning for Power-Proportional Data Centers
Energy consumption represents a significant cost in data center operation. A
large fraction of the energy, however, is used to power idle servers when the
workload is low. Dynamic provisioning techniques aim at saving this portion of
the energy, by turning off unnecessary servers. In this paper, we explore how
much performance gain can knowing future workload information brings to dynamic
provisioning. In particular, we study the dynamic provisioning problem under
the cost model that a running server consumes a fixed amount energy per unit
time, and develop online solutions with and without future workload information
available. We first reveal an elegant structure of the off-line dynamic
provisioning problem, which allows us to characterize and achieve the optimal
solution in a {}"divide-and-conquer" manner. We then exploit this insight to
design three online algorithms with competitive ratios ,
and , respectively,
where is the fraction of a critical window in which future
workload information is available. A fundamental observation is that
\emph{future workload information beyond the critical window will not}
\emph{improve dynamic provisioning performance}. Our algorithms are
decentralized and are simple to implement. We demonstrate their effectiveness
in simulations using real-world traces. We also compare their performance with
state-of-the-art solutions
Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves
In a family of curves, the Chern numbers of a singular fiber are the local
contributions to the Chern numbers of the total space. We will give some
inequalities between the Chern numbers of a singular fiber as well as their
lower and upper bounds. We introduce the dual fiber of a singular fiber, and
prove a duality theorem. As an application, we will classify singular fibers
with large or small Chern numbers.Comment: 23 page
High-dimensional robust precision matrix estimation: Cellwise corruption under -contamination
We analyze the statistical consistency of robust estimators for precision
matrices in high dimensions. We focus on a contamination mechanism acting
cellwise on the data matrix. The estimators we analyze are formed by plugging
appropriately chosen robust covariance matrix estimators into the graphical
Lasso and CLIME. Such estimators were recently proposed in the robust
statistics literature, but only analyzed mathematically from the point of view
of the breakdown point. This paper provides complementary high-dimensional
error bounds for the precision matrix estimators that reveal the interplay
between the dimensionality of the problem and the degree of contamination
permitted in the observed distribution. We also show that although the
graphical Lasso and CLIME estimators perform equally well from the point of
view of statistical consistency, the breakdown property of the graphical Lasso
is superior to that of CLIME. We discuss implications of our work for problems
involving graphical model estimation when the uncontaminated data follow a
multivariate normal distribution, and the goal is to estimate the support of
the population-level precision matrix. Our error bounds do not make any
assumptions about the the contaminating distribution and allow for a
nonvanishing fraction of cellwise contamination.Comment: 52 pages including appendi
A counterexample to the Nelson-Seiberg theorem
We present a counterexample to the Nelson-Seiberg theorem and its extensions.
The model has 4 chiral fields, including one R-charge 2 field and no R-charge 0
filed. Giving generic values of coefficients in the renormalizable
superpotential, there is a supersymmetric vacuum with one complex dimensional
degeneracy. The superpotential equals zero and the R-symmetry is broken
everywhere on the degenerated vacuum. The existence of such a vacuum disagrees
with both the original Nelson-Seiberg theorem and its extensions, and can be
viewed as the consequence of a non-generic R-charge assignment. Such
counterexamples may introduce error to the field counting method for surveying
the string landscape, and are worth further investigations.Comment: 7 pages; v2: discussion on non-generic R-charges added, new
references updated; v3: minor changes to notation and convention in formulas,
JHEP pre-publication versio
Relative Error of Scaled Poisson Approximation via Stein's Method
We study the accuracy of a scaled Poisson approximation to the weighted sum
of independent Poisson random variables, focusing on in particular the relative
error of the tail distribution. We establish a moderate deviation bound on the
approximation error using a modified Stein-Chen method. Numerical experiments
are also presented to demonstrate the quality of the approximation
Optimal Estimation of A Quadratic Functional and Detection of Simultaneous Signals
Motivated by applications in genomics, this paper studies the problem of
optimal estimation of a quadratic functional of two normal mean vectors,
, with a particular
focus on the case where both mean vectors are sparse. We propose optimal
estimators of for different regimes and establish the minimax
rates of convergence over a family of parameter spaces. The optimal rates
exhibit interesting phase transitions in this family. The simultaneous signal
detection problem is also considered under the minimax framework. It is shown
that the proposed estimators for naturally lead to optimal
testing procedures.Comment: 41 pages including appendix, 3 figures, 3 table
Standardization, Distance, Host Galaxy Extinction of Type Ia Supernova and Hubble Diagram from the Flux Ratio Method
In this paper we generalize the flux ratio method Bailey et al. (2009) to the
case of two luminosity indicators and search the optimal luminosity-flux ratio
relations on a set of spectra whose phases are around not only the date of
bright light but also other time. With these relations, a new method is
proposed to constrain the host galaxy extinction of SN Ia and its distance. It
is first applied to the low redshift supernovas and then to the high redshift
ones. The results of the low redshift supernovas indicate that the flux ratio
method can indeed give well constraint on the host galaxy extinction parameter
E(B-V), but weaker constraints on R_{V}. The high redshift supernova spectra
are processed by the same method as the low redshift ones besides some
differences due to their high redshift. Among 16 high redshift supernovas, 15
are fitted very well except 03D1gt. Based on these distances, Hubble diagram is
drew and the contents of the Universe are analyzed. It supports an acceleration
behavior in the late Universe. Therefore, the flux ratio method can give
constraints on the host galaxy extinction and supernova distance independently.
We believe, through further studies, it may provide a precise tool to probe the
acceleration of the Universe than before.Comment: 33 pages, 9 figures and 6 table
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