31,227 research outputs found
Symmetry, regression design, and sampling distributions
When values of regressors are symmetrically disposed, many M-estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased and, when moments exist, the estimators are exactly uncorrelated with estimators of other parameters. The result is unusual in that it does not require response variates to have symmetric conditional distributions. It demonstrates the potential importance of covariate design in determining the distributions of estimators, and it is useful in designing and interpreting Monte Carlo experiments. The result is illustrated by a Monte Carlo experiment in which maximum likelihood and symmetrically censored least-squares estimators are calculated for small samples from a censored normal linear regression, Tobit, model. © 1994, Cambridge University Press. All rights reserved
(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
We consider ultraweak variational formulations for (parametrized) linear
first order transport equations in time and/or space. Computationally feasible
pairs of optimally stable trial and test spaces are presented, starting with a
suitable test space and defining an optimal trial space by the application of
the adjoint operator. As a result, the inf-sup constant is one in the
continuous as well as in the discrete case and the computational realization is
therefore easy. In particular, regarding the latter, we avoid a stabilization
loop within the greedy algorithm when constructing reduced models within the
framework of reduced basis methods. Several numerical experiments demonstrate
the good performance of the new method
Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
We use simulated maps of the cosmic microwave background anisotropy to
quantify the ability of different statistical tests to discriminate between
Gaussian and non-Gaussian models. Despite the central limit theorem on large
angular scales, both the genus and extrema correlation are able to discriminate
between Gaussian models and a semi-analytic texture model selected as a
physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps,
both tests prefer the Gaussian model. Although the bispectrum has comparable
statistical power when computed on the full sky, once a Galactic cut is imposed
on the data the bispectrum loses the ability to discriminate between models.
Off-diagonal elements of the bispectrum are comparable to the diagonal elements
for the non-Gaussian texture model and must be included to obtain maximum
statistical power.Comment: Accepted for publication in ApJ; 20 pages, 6 figures, uses AASTeX
v5.
Cloud Compute-and-Forward with Relay Cooperation
We study a cloud network with M distributed receiving antennas and L users,
which transmit their messages towards a centralized decoder (CD), where M>=L.
We consider that the cloud network applies the Compute-and-Forward (C&F)
protocol, where L antennas/relays are selected to decode integer equations of
the transmitted messages. In this work, we focus on the best relay selection
and the optimization of the Physical-Layer Network Coding (PNC) at the relays,
aiming at the throughput maximization of the network. Existing literature
optimizes PNC with respect to the maximization of the minimum rate among users.
The proposed strategy maximizes the sum rate of the users allowing nonsymmetric
rates, while the optimal solution is explored with the aid of the Pareto
frontier. The problem of relay selection is matched to a coalition formation
game, where the relays and the CD cooperate in order to maximize their profit.
Efficient coalition formation algorithms are proposed, which perform joint
relay selection and PNC optimization. Simulation results show that a
considerable improvement is achieved compared to existing results, both in
terms of the network sum rate and the players' profits.Comment: Submitted to IEEE Transactions on Wireless Communication
Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
We study the phase diagram of an SU(3)-symmetric mixture of three-component
ultracold fermions with attractive interactions in an optical lattice,
including the additional effect on the mixture of an effective three-body
constraint induced by three-body losses. We address the properties of the
system in by using dynamical mean-field theory and variational Monte
Carlo techniques. The phase diagram of the model shows a strong interplay
between magnetism and superfluidity. In the absence of the three-body
constraint (no losses), the system undergoes a phase transition from a color
superfluid phase to a trionic phase, which shows additional particle density
modulations at half-filling. Away from the particle-hole symmetric point the
color superfluid phase is always spontaneously magnetized, leading to the
formation of different color superfluid domains in systems where the total
number of particles of each species is conserved. This can be seen as the SU(3)
symmetric realization of a more general tendency to phase-separation in
three-component Fermi mixtures. The three-body constraint strongly disfavors
the trionic phase, stabilizing a (fully magnetized) color superfluid also at
strong coupling. With increasing temperature we observe a transition to a
non-magnetized SU(3) Fermi liquid phase.Comment: 36 pages, 17 figures; Corrected typo
Coarse-Graining and Renormalization Group in the Einstein Universe
The Kadanoff-Wilson renormalization group approach for a scalar
self-interacting field theor generally coupled with gravity is presented. An
average potential that monitors the fluctuations of the blocked field in
different scaling regimes is constructed in a nonflat background and explicitly
computed within the loop-expansion approximation for an Einstein universe. The
curvature turns out to be dominant in setting the crossover scale from a
double-peak and a symmetric distribution of the block variables. The evolution
of all the coupling constants generated by the blocking procedure is examined:
the renormalized trajectories agree with the standard perturbative results for
the relevant vertices near the ultraviolet fixed point, but new effective
interactions between gravity and matter are present. The flow of the conformal
coupling constant is therefore analyzed in the improved scheme and the infrared
fixed point is reached for arbitrary values of the renormalized parameters.Comment: 18 pages, REVTex, two uuencoded figures. (to appear in Phys. Rev.
D15, July) Transmission errors have been correcte
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