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

Metamaterial nanotips

Nanostructured metamaterials, especially arrays of metallic nanoparticles which sustain the excitation of localized plasmon polaritons, provide excellent opportunities to mold the flow of light in the linear regime. We suggest a metamaterial structure whose properties are determined not only by its inner geometry but also by its entire shape. We call this structure a \emph{metamaterial nanotip}. We evaluate the potential of this nanotip to control the size and the location of the field enhancement. Two-dimensional implementations of this metamaterial nanotip were comprehensively numerically simulated and confirm the expected, physically distinct regimes of operation.Comment: 4 pages, 4 figure

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 $4.15 < nu < 4.26$, 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)

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

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

Asymmetric transmission of linearly polarized light at optical metamaterials

We experimentally demonstrate a three-dimensional chiral optical metamaterial that exhibits an asymmetric transmission for forwardly and backwardly propagating linearly polarized light. The observation of this novel effect requires a metamaterial composed of three-dimensional chiral metaatoms without any rotational symmetry. Our analysis is supported by a systematic investigation of the transmission matrices for arbitrarily complex, lossy media that allows deriving a simple criterion for asymmetric transmission in an arbitrary polarization base. Contrary to physical intuition, in general the polarization eigenstates in such three-dimensional and low-symmetry metamaterials do not obey fxed relations and the associated transmission matrices cannot be symmetrized

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 $L^2$-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 $\mathrm{curl}$ 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

Average Run Length and Mean Delay for Changepoint Detection: Robust Estimates for Threshold Alarms

Online Monitoring is a rapidly expanding field in different areas such as quality control, finance and navigation. The automated detection of so-called changepoints is playing a prominent role in all these fields, be it the detection of sudden shifts of the mean of a continuously monitored quantity, the variance of stock quotes or the change of some characteristic features indicating the malfunctioning of one of the detectors used for navigation (the ``faulty sensor problem''). A prominent example for the application of advanced statistical methods for the detection of changepoints in biomedical time series is the multi-process Kalman filter used by Smith and West [Smith 1983] to monitor renal transplants. However, despite the fact that the algorithm could be tuned in such a way that the computer could predict dangerous situations on the average one day before the human experts it has nevertheless become superfluous as soon as new diagnosic tools became available. Many of the automated monitoring systems which are widely used in practice are based on simple threshold alarms. Some upper and lower limits are chosen at the beginning of the monitoring session and an alarm is triggered whenever the measured values exceed the upper limit or fall below the lower limit. This is e.g. common practice for the monitoring of patients during surgery, where such thresholds are chosen for heart rate, blood pressure etc. by the anaesthesist. The fate of the multi-process Kalman filter for monitoring renal transplants teaches two lessons: first, there is considerable power in statistical methods to improve conventional biomedical monitoring techniques. Second, if the statistical model and the methods are too refined they may never be used in practice. We shall suggest a stochastic model for changepoints which we have found to have the capacity to be very useful in practice, i.e. which is sufficiently complex to cover the important features of a changepoint system but simple enough to be understandable and adaptible. We focus our attention on the properties of the threshold alarm for different values of the parameters of the threshold alarm and the model. This will give us practically relevant estimates for this important class of alarm systems and moreover a benchmark for the evaluation of competing alternative algorithms. Note that virtually every algorithm designed to detect changepoints is based on a threshold alarm, the only difference being that the threshold alarm is not fed with the original data but by a transformation thereof, usually called ``residuum'' [Basseville 1993]. As a general measure for quality, we look on the one hand at the mean delay time $\tau$ between a changepoint and its detection and on the other hand at the mean waiting time for a false alarm, the so-called average run length ARL