Finite-temperature Bell test for quasiparticle entanglement in the Fermi sea

We demonstrate that the Bell test cannot be realized at finite temperatures in the vast majority of electronic setups proposed previously for quantum entanglement generation. This fundamental difficulty is shown to originate in a finite probability of quasiparticle emission from Fermi-sea detectors. In order to overcome the feedback problem, we suggest a detection strategy, which takes advantage of a resonant coupling to the quasiparticle drains. Unlike other proposals, the designed Bell test provides a possibility to determine the critical temperature for entanglement production in the solid state.Comment: 6 pages, 3 figures, essentially revised and extended versio

Can one estimate the conditional distribution of post-model-selection estimators?

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.Comment: Published at http://dx.doi.org/10.1214/009053606000000821 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing in the Presence of Nuisance Parameters: Some Comments on Tests Post-Model-Selection and Random Critical Values

We point out that the ideas underlying some test procedures recently proposed for testing post-model-selection (and for some other test problems) in the econometrics literature have been around for quite some time in the statistics literature. We also sharpen some of these results in the statistics literature. Furthermore, we show that some intuitively appealing testing procedures, that have found their way into the econometrics literature, lead to tests that do not have desirable size properties, not even asymptotically.Comment: Minor revision. Some typos and errors corrected, some references adde

A Dynamic Model of the Environmental Kuznets Curve : Turning Point and Public Poliy

We set up a simple dynamic macroeconomic model with (i) polluting consump- tion and a preference for a clean environment, (ii) increasing returns in abate- ment giving rise to an EKC and (iii) sustained growth resulting from a linear final-output technology. The model captures two sorts of market failures caused by external effects associated with consumption and environmental effort. This model is employed to investigate the determinants of the turning point and the (relative) effectiveness of different public policy measures aimed at a reduction of the environmental burden. Moreover, the model offers a potential explana- tion of an N-shaped pollution-income relation. Finally, it is shown that the model is compatible with most empirical regularities on economic growth and the environment.Environmental Kuznets Curve, Pollution, Abatement, External Ef- fects, Economic Growth, Public Policy

Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion like AIC or by a hypothesis testing procedure) and second estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.Inference after model selection, Post-model-selection estimator, Pre-test estimator, Selection of regressors, Akaikeis information criterion AIC, Model uncertainty, Consistency, Uniform consistency, Lower risk bound

Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator

We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges’ estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity when ever the loss function is unbounded. For ease of presentation the result is set in the framework of a linear regression model, but generalizes far beyond that setting. In a Monte Carlo study we also assess the extent of the problem infinite samples for the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001). We find that this estimator can perform rather poorly infinite samples and that its worst-case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity.Oracle property, Sparsity, Penalized maximum likelihood, Penalized least squares, Hodges’ estimator, SCAD, Lasso, Bridge estimator, Hard-thresholding, Maximal risk, Maximal absolute bias, Non-uniform limits

pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems

pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu's problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from www.staff.uni-oldenburg.de/hannes.uecker/pde2path, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems