Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment. A supplement to this paper which contains additional technical proofs is available online.Comment: To appear in Journal of the American Statistical Associatio

Spin-injection Hall effect in a planar photovoltaic cell

Successful incorporation of the spin degree of freedom in semiconductor technology requires the development of a new paradigm allowing for a scalable, non-destructive electrical detection of the spin-polarization of injected charge carriers as they propagate along the semiconducting channel. In this paper we report the observation of a spin-injection Hall effect (SIHE) which exploits the quantum-relativistic nature of spin-charge transport and which meets all these key requirements on the spin detection. The two-dimensional electron-hole gas photo-voltaic cell we designed to observe the SIHE allows us to develop a quantitative microscopic theory of the phenomenon and to demonstrate its direct application in optoelectronics. We report an experimental realization of a non-magnetic spin-photovoltaic effect via the SIHE, rendering our device an electrical polarimeter which directly converts the degree of circular polarization of light to a voltage signal.Comment: 14 pages, 4 figure

Thermodynamic Geometry and Critical Behavior of Black Holes

Based on the observations that there exists an analogy between the Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is $(\phi, q) \leftrightarrow (V,P)$, we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN-AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN-AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.Comment: Revtex, 18 pages including 4 figure

Completeness Results for Parameterized Space Classes

The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have, however, resisted such a classification. At least in some cases, the reason is that upper and lower bounds for their parameterized space complexity have recently been obtained that rule out completeness results for parameterized time classes. In this paper, we make progress in this direction by proving that the associative generability problem and the longest common subsequence problem are complete for parameterized space classes. These classes are defined in terms of different forms of bounded nondeterminism and in terms of simultaneous time--space bounds. As a technical tool we introduce a "union operation" that translates between problems complete for classical complexity classes and for W-classes.Comment: IPEC 201

Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis

To investigate whether treating cancer patients with erythropoiesis-stimulating agents (ESAs) would increase the mortality risk, Bennett et al. [Journal of the American Medical Association 299 (2008) 914--924] conducted a meta-analysis with the data from 52 phase III trials comparing ESAs with placebo or standard of care. With a standard parametric random effects modeling approach, the study concluded that ESA administration was significantly associated with increased average mortality risk. In this article we present a simple nonparametric inference procedure for the distribution of the random effects. We re-analyzed the ESA mortality data with the new method. Our results about the center of the random effects distribution were markedly different from those reported by Bennett et al. Moreover, our procedure, which estimates the distribution of the random effects, as opposed to just a simple population average, suggests that the ESA may be beneficial to mortality for approximately a quarter of the study populations. This new meta-analysis technique can be implemented with study-level summary statistics. In contrast to existing methods for parametric random effects models, the validity of our proposal does not require the number of studies involved to be large. From the results of an extensive numerical study, we find that the new procedure performs well even with moderate individual study sample sizes.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS280 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

"Microscopic" approach to the Ricci dark energy

A derivation of the Ricci dark energy from quantum field theory of fluctuating "matter" fields in a classical gravitational background is presented. The coupling to the dark energy, the parameter 'a', is estimated in the framework of our formalism, and qualitatively it appears to be within observational expectations.Comment: 7 page