Higher-order expansions of powered extremes of normal samples

In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions/densities of normalized extremes depends in principle on the power index

Generation of large-scale magnetic fields from inflation in teleparallelism

We explore the generation of large-scale magnetic fields from inflation in teleparallelism, in which the gravitational theory is described by the torsion scalar instead of the scalar curvature in general relativity. In particular, we examine the case that the conformal invariance of the electromagnetic field during inflation is broken by a non-minimal gravitational coupling between the torsion scalar and the electromagnetic field. It is shown that for a power-law type coupling, the magnetic field on 1 Mpc scale with its strength of $\sim 10^{-9}$ G at the present time can be generated.Comment: 18 pages, no figure, version accepted for publication in JCA

Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization

We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging, optics, and wireless communications. A key challenge of this intricate non-convex optimization problem is that it might exhibit many local minima. We present an efficient numerical algorithm that is guaranteed to recover the exact solution, when the number of measurements is (up to log-factors) slightly larger than the information-theoretical minimum, and under reasonable conditions on $f$ and $g$. The proposed regularized gradient descent algorithm converges at a geometric rate and is provably robust in the presence of noise. To the best of our knowledge, our algorithm is the first blind deconvolution algorithm that is numerically efficient, robust against noise, and comes with rigorous recovery guarantees under certain subspace conditions. Moreover, numerical experiments do not only provide empirical verification of our theory, but they also demonstrate that our method yields excellent performance even in situations beyond our theoretical framework

The Lending-Deposit Rate Relationship in Eastern European Countries: Evidence from the Rank Test for Non-linear Cointegration

This study carries out an examination of the potential non-linear cointegration between the lending and deposit rates of eight Eastern European countries using the non-parametric rank tests proposed by Breitung (2001). Based upon our adoption in this study of the threshold error-correction model (TECM), we find solid evidence of an asymmetric price transmission effect, in both the short term and the long term, between lending and deposit rates. Thus, our results reveal that there are indeed such long-run non-linear cointegration relationships between the lending and deposit rates in these Eastern European countries. Furthermore, we go on to successfully capture the dynamic adjustment of the spread.lending-deposit rates, rank test, non-linearity