17,761 research outputs found
P-T phase diagram of a holographic s+p model from Gauss-Bonnet gravity
In this paper, we study the holographic s+p model in 5-dimensional bulk
gravity with the Gauss-Bonnet term. We work in the probe limit and give the
-T phase diagrams at three different values of the Gauss-Bonnet
coefficient to show the effect of the Gauss-Bonnet term. We also construct the
P-T phase diagrams for the holographic system using two different definitions
of the pressure and compare the results.Comment: 17 pages, 5 figures, we have added new P-T phase diagrams with the
pressure defined in boundary stress-energy tenso
Optimality of Graphlet Screening in High Dimensional Variable Selection
Consider a linear regression model where the design matrix X has n rows and p
columns. We assume (a) p is much large than n, (b) the coefficient vector beta
is sparse in the sense that only a small fraction of its coordinates is
nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row
has relatively few large coordinates (diagonals of G are normalized to 1).
The sparsity in G naturally induces the sparsity of the so-called graph of
strong dependence (GOSD). We find an interesting interplay between the signal
sparsity and the graph sparsity, which ensures that in a broad context, the set
of true signals decompose into many different small-size components of GOSD,
where different components are disconnected.
We propose Graphlet Screening (GS) as a new approach to variable selection,
which is a two-stage Screen and Clean method. The key methodological innovation
of GS is to use GOSD to guide both the screening and cleaning. Compared to
m-variate brute-forth screening that has a computational cost of p^m, the GS
only has a computational cost of p (up to some multi-log(p) factors) in
screening.
We measure the performance of any variable selection procedure by the minimax
Hamming distance. We show that in a very broad class of situations, GS achieves
the optimal rate of convergence in terms of the Hamming distance. Somewhat
surprisingly, the well-known procedures subset selection and the lasso are rate
non-optimal, even in very simple settings and even when their tuning parameters
are ideally set
Stability Condition of a Strongly Interacting Boson-Fermion Mixture across an Inter-Species Feshbach Resonance
We study the properties of dilute bosons immersed in a single component Fermi
sea across a broad boson-fermion Feshbach resonance. The stability of the
mixture requires that the bare interaction between bosons exceeds a critical
value, which is a universal function of the boson-fermion scattering length,
and exhibits a maximum in the unitary region. We calculate the quantum
depletion, momentum distribution and the boson contact parameter across the
resonance. The transition from condensate to molecular Fermi gas is also
discussed.Comment: 4 pages, 4 figure
Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
We continue the study of the nonconforming multiscale finite element method (Ms- FEM) introduced in 17, 14 for second order elliptic equations with highly oscillatory coefficients. The main difficulty in MsFEM, as well as other numerical upscaling methods, is the scale resonance effect. It has been show that the leading order resonance error can be effectively removed by using an over-sampling technique. Nonetheless, there is still a secondary cell resonance error of O(Š^2/h^2). Here, we introduce a Petrov-Galerkin MsFEM formulation with nonconforming multiscale trial functions and linear test functions. We show that the cell resonance error is eliminated in this formulation and hence the convergence rate is greatly improved. Moreover, we show that a similar formulation can be used to enhance the convergence of an immersed-interface finite element method for elliptic interface problems
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