3,371 research outputs found
How Correlations Influence Lasso Prediction
We study how correlations in the design matrix influence Lasso prediction.
First, we argue that the higher the correlations are, the smaller the optimal
tuning parameter is. This implies in particular that the standard tuning
parameters, that do not depend on the design matrix, are not favorable.
Furthermore, we argue that Lasso prediction works well for any degree of
correlations if suitable tuning parameters are chosen. We study these two
subjects theoretically as well as with simulations
Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
Recent works showed that pressure-robust modifications of mixed finite
element methods for the Stokes equations outperform their standard versions in
many cases. This is achieved by divergence-free reconstruction operators and
results in pressure independent velocity error estimates which are robust with
respect to small viscosities. In this paper we develop a posteriori error
control which reflects this robustness.
The main difficulty lies in the volume contribution of the standard
residual-based approach that includes the -norm of the right-hand side.
However, the velocity is only steered by the divergence-free part of this
source term. An efficient error estimator must approximate this divergence-free
part in a proper manner, otherwise it can be dominated by the pressure error.
To overcome this difficulty a novel approach is suggested that uses arguments
from the stream function and vorticity formulation of the Navier--Stokes
equations. The novel error estimators only take the of the
right-hand side into account and so lead to provably reliable, efficient and
pressure-independent upper bounds in case of a pressure-robust method in
particular in pressure-dominant situations. This is also confirmed by some
numerical examples with the novel pressure-robust modifications of the
Taylor--Hood and mini finite element methods
Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
In the framework of a recently developed model of interacting composite
fermions, we calculate the energy of different solid and Laughlin-type liquid
phases of spin-polarized composite fermions. The liquid phases have a lower
energy than the competing solids around the electronic filling factors
nu=4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum
Hall effect at nu=4/11. The alternation between solid and liquid phases when
varying the magnetic field may lead to reentrance phenomena in analogy with the
observed reentrant integral quantum Hall effect.Comment: 4 pages, 3 figures; revised version accepted for publication in Phys.
Rev. Let
Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect
A recently developed model of interacting composite fermions, is used to
investigate different composite-fermion phases. Their interaction potential
allows for the formation of both solid and new quantum-liquid phases, which are
interpreted in terms of second-generation composite fermions and which may be
responsible for the fractional quantum Hall states observed at unusual filling
factors, such as nu=4/11. Projection of the composite-fermion dynamics to a
single level, involved in the derivation of the Hamiltonian of interacting
composite fermions, reveals the underlying self-similarity of the model.Comment: 4 pages, 1 figure; to appear in "Proceedings of the 16th
International Conference on High Magnetic Fields in Semiconductor Physics
(SemiMag-16)", only change with respect to v1: correction in authors line, no
changes in manuscrip
Quantum Phases in Partially Filled Landau Levels
We compare the energies of different electron solids, such as bubble crystals
with triangular and square symmetry and stripe phases, to those of correlated
quantum liquids in partially filled intermediate Landau levels. Multiple
transitions between these phases when varying the filling of the top-most
partially filled Landau level explain the observed reentrance of the integer
quantum Hall effect. The phase transitions are identified as first-order. This
leads to a variety of measurable phenomena such as the phase coexistence
between a Wigner crystal and a two-electron bubble phase in a Landau-level
filling-factor range , which has recently been observed in
transport measurements under micro-wave irradiation.Comment: 6 pages, 2 figures; to appear in "Proceedings of the 16th
International Conference on High Magnetic Fields in Semiconductor Physics
(SemiMag-16)
Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study
The Field Induced Spin Density Wave phases observed in quasi-one-dimensional
conductors of the Bechgaard salts family under magnetic field exhibit both Spin
Density Wave order and a Quantized Hall Effect, which may exhibit sign
reversals. The original nature of the condensed phases is evidenced by the
collective mode spectrum. Besides the Goldstone modes, a quasi periodic
structure of Magneto-Roton modes, predicted to exist for a monotonic sequence
of Hall Quantum numbers, is confirmed, and a second mode is shown to exist
within the single particle gap. We present numerical estimates of the
Magneto-Roton mode energies in a generic case of the monotonic sequence. The
mass anisotropy of the collective mode is calculated. We show how differently
the MR spectrum evolves with magnetic field at low and high fields. The
collective mode spectrum should have specific features, in the sign reversed
"Ribault Phase", as compared to modes of the majority sign phases. We
investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat
preprint cond-mat/9709210, but cannot be described as a replaced version,
because it contains a significant amount of new material dealing with the
instability line and with the topic of Ribault Phases. It contains 13 figures
(.ps files
Multiple sclerosis, the measurement of disability and access to clinical trial data
Background: Inferences about long-term effects of therapies in multiple sclerosis (MS) have been based on surrogate markers studied in short-term trials. Nevertheless, MS trials have been getting steadily shorter despite the lack of a consensus definition for the most important clinical outcome - unremitting progression of disability. Methods: We have examined widely used surrogate markers of disability progression in MS within a unique database of individual patient data from the placebo arms of 31 randomised clinical trials. Findings: Definitions of treatment failure used in secondary progressive MS trials include much change unrelated to the target of unremitting disability. In relapsing-remitting MS, disability progression by treatment failure definitions was no more likely than similarly defined improvement for these disability surrogates. Existing definitions of disease progression in relapsing-remitting trials encompass random variation, measurement error and remitting relapses and appear not to measure unremitting disability. Interpretation: Clinical surrogates of unremitting disability used in relapsing -remitting trials cannot be validated. Trials have been too short and/or degrees of disability change too small to evaluate unremitting disability outcomes. Important implications for trial design and reinterpretation of existing trial results have emerged long after regulatory approval and widespread use of therapies in MS, highlighting the necessity of having primary trial data in the public domain
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