55,411 research outputs found
The Nature and Validity of the RKKY limit of exchange coupling in magnetic trilayers
The effects on the exchange coupling in magnetic trilayers due to the
presence of a spin-independent potential well are investigated. It is shown
that within the RKKY theory no bias nor extra periods of oscillation associated
with the depth of the well are found, contrary to what has been claimed in
recent works. The range of validity of the RKKY theory is also discussed.Comment: 10, RevTe
A computational approach to the D-module of meromorphic functions
Let be a divisor in . We present methods to compare the
-module of the meromorphic functions to some
natural approximations. We show how the analytic case can be treated with
computations in the Weyl algebra.Comment: 11 page
Multiple Testing and Variable Selection along Least Angle Regression's path
In this article, we investigate multiple testing and variable selection using
Least Angle Regression (LARS) algorithm in high dimensions under the Gaussian
noise assumption. LARS is known to produce a piecewise affine solutions path
with change points referred to as knots of the LARS path. The cornerstone of
the present work is the expression in closed form of the exact joint law of
K-uplets of knots conditional on the variables selected by LARS, namely the
so-called post-selection joint law of the LARS knots. Numerical experiments
demonstrate the perfect fit of our finding.
Our main contributions are three fold. First, we build testing procedures on
variables entering the model along the LARS path in the general design case
when the noise level can be unknown. This testing procedures are referred to as
the Generalized t-Spacing tests (GtSt) and we prove that they have exact
non-asymptotic level (i.e., Type I error is exactly controlled). In that way,
we extend a work from (Taylor et al., 2014) where the Spacing test works for
consecutive knots and known variance. Second, we introduce a new exact multiple
false negatives test after model selection in the general design case when the
noise level can be unknown. We prove that this testing procedure has exact
non-asymptotic level for general design and unknown noise level. Last, we give
an exact control of the false discovery rate (FDR) under orthogonal design
assumption. Monte-Carlo simulations and a real data experiment are provided to
illustrate our results in this case. Of independent interest, we introduce an
equivalent formulation of LARS algorithm based on a recursive function.Comment: 62 pages; new: FDR control and power comparison between Knockoff,
FCD, Slope and our proposed method; new: the introduction has been revised
and now present a synthetic presentation of the main results. We believe that
this introduction brings new insists compared to previous version
Tests for the asymptotic behaviour of the gamma^* --> gamma pi^0 form factor
The gamma^* --> gamma pi^0 transition measured at different photon
virtualities already provides us with a clean test for the behaviour of the
pi^0 gamma^* gamma off-shell axial anomaly at large time-like squared momenta.
It also allows reliable predictions for the branching ratio of heavy quarkonium
decays into omega pi^0.Comment: Latex, 7 pages + 1 .ps figure, comments on the Brodsky-Lepage limit
and 5 new references adde
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