Persistent currents in a bosonic mixture in the ring geometry

In this paper we analyze the possibility of persistent currents of a two-species bosonic mixture in the one-dimensional ring geometry. We extend the arguments used by Bloch to obtain a criterion for the stability of persistent currents for the two-species system. If the mass ratio of the two species is a rational number, persistent currents can be stable at multiples of a certain total angular momenta. We show that the Bloch criterion can also be viewed as a Landau criterion involving the elementary excitations of the system. Our analysis reveals that persistent currents at higher angular momenta are more stable for the two-species system than previously thought.Comment: 20 pages and 7 figure

Quantile forecast discrimination ability and value

While probabilistic forecast verification for categorical forecasts is well established, some of the existing concepts and methods have not found their equivalent for the case of continuous variables. New tools dedicated to the assessment of forecast discrimination ability and forecast value are introduced here, based on quantile forecasts being the base product for the continuous case (hence in a nonparametric framework). The relative user characteristic (RUC) curve and the quantile value plot allow analysing the performance of a forecast for a specific user in a decision-making framework. The RUC curve is designed as a user-based discrimination tool and the quantile value plot translates forecast discrimination ability in terms of economic value. The relationship between the overall value of a quantile forecast and the respective quantile skill score is also discussed. The application of these new verification approaches and tools is illustrated based on synthetic datasets, as well as for the case of global radiation forecasts from the high resolution ensemble COSMO-DE-EPS of the German Weather Service

Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

On the Largest Singular Values of Random Matrices with Independent Cauchy Entries

We apply the method of determinants to study the distribution of the largest singular values of large $m \times n$ real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a factor of \frac{1}{m^2\*n^2})largest singular values agree in the limit with the statistics of the inhomogeneous Poisson random point process with the intensity $\frac{1}{\pi} x^{-3/2}$ and, therefore, are different from the Tracy-Widom law. Among other corollaries of our method we show an interesting connection between the mathematical expectations of the determinants of complex rectangular $m \times n$ standard Wishart ensemble and real rectangular $2m \times 2n$ standard Wishart ensemble.Comment: We have shown in the revised version that the statistics of the largest eigenavlues of a sample covariance random matrix with i.i.d. Cauchy entries agree in the limit with the statistics of the inhomogeneous Poisson random point process with the intensity $\frac{1}{\pi} x^{-3/2}.

Correlation effects in Ni 3d states of LaNiPO

The electronic structure of the new superconducting material LaNiPO experimentally probed by soft X-ray spectroscopy and theoretically calculated by the combination of local density approximation with Dynamical Mean-Field Theory (LDA+DMFT) are compared herein. We have measured the Ni L2,3 X-ray emission (XES) and absorption (XAS) spectra which probe the occupied and unoccupied the Ni 3d states, respectively. In LaNiPO, the Ni 3d states are strongly renormalized by dynamical correlations and shifted about 1.5 eV lower in the valence band than the corresponding Fe 3d states in LaFeAsO. We further obtain a lower Hubbard band at -9 eV below the Fermi level in LaNiPO which bears striking resemblance to the lower Hubbard band in the correlated oxide NiO, while no such band is observed in LaFeAsO. These results are also supported by the intensity ratio between the transition metal L2 and L3 bands measured experimentally to be higher in LaNiPO than in LaFeAsO, indicating the presence of the stronger electron correlations in the Ni 3d states in LaNiPO in comparison with the Fe 3d states in LaFeAsO. These findings are in accordance with resonantly excited transition metal L3 X-ray emission spectra which probe occupied metal 3d-states and show the appearance of the lower Hubbard band in LaNiPO and NiO and its absence in LaFeAsO.Comment: 6 pages, 5 figure

A Decision-tree Approach to Seasonal Prediction of Extreme Precipitation in Eastern China

Seasonal prediction of extreme precipitation has long been a challenge especially for the East Asian Summer Monsoon region, where extreme rains are often disastrous for the human society and economy. This paper introduces a decision‐tree (DT) method for predicting extreme precipitation in the rainy season over South China in April–June (SC‐AMJ) and the North China Plain in July–August (NCP‐JA). A number of preceding climate indices are adopted as predictors. In both cases, the DT models involving ENSO and NAO indices exhibit the best performance with significant skills among those with other combinations of predictors and are superior to their linear counterpart, the binary logistic regression model. The physical mechanisms for the DT results are demonstrated by composite analyses of the same DT path samples. For SC‐AMJ, an extreme season can be determined mainly via two paths: the first follows a persistent negative NAO phase in February–March; the second goes with decaying El Niño. For NCP‐JA, an extreme season can also be traced via two paths: the first is featured by “non El Niño” and an extremely negative NAO phase in the preceding winter; the second follows a shift from El Niño in the preceding winter to La Niña in the early summer. Most of the mechanisms underlying the decision rules have been documented in previous studies, while some need further studies. The present results suggest that the decision‐tree approach takes advantage of discovering and incorporating various nonlinear relationships in the climate system, hence is of great potential for improving the prediction of seasonal extreme precipitation for given regions with increasing sample observations

Estimations of electron-positron pair production at high-intensity laser interaction with high-Z targets

Electron-positron pairs' generation occuring in the interaction of $10^{18}$-$10^{20}$~W/cm$^2$ laser radiation with high-Z targets are examined. Computational results are presented for the pair production and the positron yield from the target with allowance for the contribution of pair production processes due to electrons and bremsstrahlung photons. Monte-Carlo simulations using the PRIZMA code confirm the estimates obtained. The possible positron yield from high-Z targets irradiated by picosecond lasers of power $10^2$-$10^3$~TW is estimated to be $10^9$-$10^{11}$