Simplified simplicial depth for regression and autoregressive growth processes

We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified simplicial depth notions are normal distributions so that tests and confidence intervals can be derived easily. We propose two simplifications for the general case and a third simplification for the special case where two parameters are unknown. Additionally, we derive conditions for the consistency of the tests. We show that the simplified depth notions can be used for polynomial regression, for several nonlinear regression models, and for several autoregressive growth processes. We compare the efficiency and robustness of the different simplified versions by a simulation study concerning the Michaelis-Menten model and a nonlinear autoregressive process of order one

Optical Response of Grating-Coupler-Induced Intersubband Resonances: The Role of Wood's Anomalies

Grating-coupler-induced collective intersubband transitions in a quasi-two-dimensional electron system are investigated both experimentally and theoretically. Far-infrared transmission experiments are performed on samples containing a quasi-two-dimensional electron gas quantum-confined in a parabolic quantum well. For rectangular shaped grating couplers of different periods we observe a strong dependence of the transmission line shape and peak height on the period of the grating, i.e. on the wave vector transfer from the diffracted beams to the collective intersubband resonance. It is shown that the line shape transforms with increasing grating period from a Lorentzian into a strongly asymmetric line shape. Theoretically, we treat the problem by using the transfer-matrix method of local optics and apply the modal-expansion method to calculate the influence of the grating. The optically uniaxial quasi-two-dimensional electron gas is described in the long-wavelength limit of the random-phase approximation by a local dielectric tensor, which includes size quantization effects. Our theory reproduces excellently the experimental line shapes. The deformation of the transmission line shapes we explain by the occurrence of both types of Wood's anomalies.Comment: 28 pages, 7 figures. Physical Review B , in pres

Biofortification and subcellular localization of minerals in faba bean as influenced by Mg foliar application

Foliar application of Mg is a measure for the correction of Mg deficiency in crop plants. Foliar applied nutrients need to access the symplastic side where majority of physiological processes take place. To achieve an adequate uptake of the Mg ions through the leaf surface, high concentrations of of 100-200 mM MgSO4 are usually supplied. This can cause antagonistic perturbations on the subcellular distribution of Caand K cations. To test for such unintended side effects, we used the infiltration-centrifugation method to extract ions from the apoplastic and symplastic side of Vicia faba leaves and quantified concentrations of Mg, Ca and K in dependency to the dose of the foliar fertilized Mg. Results show that a large fraction of Mg accesses the symplast whereas the apoplastic fraction shows a concomitant increase. Symplastic and apoplastic K and Ca relations were only affected under conditions of high exogenous leaf supply of Mg (200 mM) but did not change upon moderate Mg supply (50; 100 mM). Overall, results reveal the suitability of leaf fertilization to biofortify plant-based products with magnesium. With respect to human nutrition, care must be taken that K and Ca do not become impoverished based on antagonistic effects

Microscopic view on Landau level broadening mechanisms in graphene

Placing a two-dimensional sheet of graphene in an external magnetic field the continuous electronic band structure is discretized due to Landau quantization. The resulting optical transitions are subject to a broadening, which can lead to a significant overlap of Landau levels. We investigate the possible microscopic processes that could cause a broadening of the corresponding peaks in the absorption spectrum of Landau-quantized graphene: (i) radiative decay, (ii) Coulomb interaction, (iii) optical phonons, (iv) acoustic phonons, and (v) impurities. Since recent experiments have shown that independent of the magnetic field the resolvable number of Landau levels is constant, we put a special focus on the dependence of the broadening on the external magnetic field B and the Landau level index n. Our calculations reveal the impurities to be the crucial broadening mechanism, where different regimes of well separated and densely spaced Landau levels need to be taken into account. Furthermore, carrier-carrier and carrier-phonon scattering give rise to a very specific dependence on the Landau level index n that has not been observed yet

Localized magnetoplasmon modes arising from broken translational symmetry in semiconductor superlattices

The electromagnetic propagator associated with the localized collective magnetoplasmon excitations in a semiconductor superlattice with broken translational symmetry, is calculated analytically within linear response theory. We discuss the properties of these collective excitations in both radiative and non-radiative regimes of the electromagnetic spectra. We find that low frequency retarded modes arise when the surface density of carriers at the symmetry breaking layer is lower than the density at the remaining layers. Otherwise a doublet of localized, high-frequency magnetoplasmon-like modes occurs.Comment: Revtex file + separate pdf figure

A possible cooling effect in high temperature superconductors

We show that an adiabatic increase of the supercurrent along a superconductor with lines of nodes of the order parameter on the Fermi surface can result in a cooling effect. The maximum cooling occurs if the supercurrent increases up to its critical value. The effect can also be observed in a mixed state of a bulk sample. An estimate of the energy dissipation shows that substantial cooling can be performed during a reasonable time even in the microkelvin regime.Comment: 5 pages, to appear in Phys. Rev.

Jahn-Teller stabilization of a "polar" metal oxide surface: Fe3O4(001)

Using ab initio thermodynamics we compile a phase diagram for the surface of Fe3O4(001) as a function of temperature and oxygen pressures. A hitherto ignored polar termination with octahedral iron and oxygen forming a wave-like structure along the [110]-direction is identified as the lowest energy configuration over a broad range of oxygen gas-phase conditions. This novel geometry is confirmed in a x-ray diffraction analysis. The stabilization of the Fe3O4(001)-surface goes together with dramatic changes in the electronic and magnetic properties, e.g., a halfmetal-to-metal transition.Comment: 4 pages, 4 figure

Mean parameter model for the Pekar-Fr\"{o}hlich polaron in a multilayered heterostructure

The polaron energy and the effective mass are calculated for an electron confined in a finite quantum well constructed of $GaAs/Al_x Ga_{1-x} As$ layers. To simplify the study we suggest a model in which parameters of a medium are averaged over the ground-state wave function. The rectangular and the Rosen-Morse potential are used as examples. To describe the confined electron properties explicitly to the second order of perturbations in powers of the electron-phonon coupling constant we use the exact energy-dependent Green function for the Rosen-Morse confining potential. In the case of the rectangular potential, the sum over all intermediate virtual states is calculated. The comparison is made with the often used leading term approximation when only the ground-state is taken into account as a virtual state. It is shown that the results are quite different, so the incorporation of all virtual states and especially those of the continuous spectrum is essential. Our model reproduces the correct three-dimensional asymptotics at both small and large widths. We obtained a rather monotonous behavior of the polaron energy as a function of the confining potential width and found a peak of the effective mass. The comparison is made with theoretical results by other authors. We found that our model gives practically the same (or very close) results as the explicit calculations for potential widths $L \geq 10 \AA$.Comment: 12 pages, LaTeX, including 5 PS-figures, subm. to Phys. Rev. B, new data are discusse