Optimal rates of convergence for covariance matrix estimation

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm. It is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation. The minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties. A key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound. The technical analysis requires new ideas that are quite different from those used in the more conventional function/sequence estimation problems.Comment: Published in at http://dx.doi.org/10.1214/09-AOS752 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Photon-assisted electron transmission resonance through a quantum well with spin-orbit coupling

Using the effective-mass approximation and Floquet theory, we study the electron transmission over a quantum well in semiconductor heterostructures with Dresselhaus spin-orbit coupling and an applied oscillation field. It is demonstrated by the numerical evaluations that Dresselhaus spin-orbit coupling eliminates the spin degeneracy and leads to the splitting of asymmetric Fano-type resonance peaks in the conductivity. In turn, the splitting of Fano-type resonance induces the spin- polarization-dependent electron-current. The location and line shape of Fano-type resonance can be controlled by adjusting the oscillation frequency and the amplitude of external field as well. These interesting features may be a very useful basis for devising tunable spin filters.Comment: 10pages,4figure

Periodontitis-induced systemic inflammation exacerbates atherosclerosis partly via endothelial-mesenchymal transition in mice.

Growing evidence suggests close associations between periodontitis and atherosclerosis. To further understand the pathological relationships of these associations, we developed periodontitis with ligature placement around maxillary molars or ligature placement in conjunction with Porphyromonas gingivalis lipopolysaccharide injection at the ligature sites (ligature/P.g. LPS) in Apolipoprotein E knock out mice and studied the atherogenesis process in these animals. The mice were fed with high fat diet for 11 weeks and sacrificed for analyzing periodontitis, systemic inflammation, and atherosclerosis. Controls did not develop periodontitis or systemic inflammation and had minimal lipid deposition in the aortas, but mice receiving ligature or ligature/P.g. LPS showed severe periodontitis, systemic inflammation, and aortic plaque formation. The aortic plaque contained abundant macrophages and cells expressing both endothelial and mesenchymal cell markers. The severity of periodontitis was slightly higher in mice receiving ligature/P.g. LPS than ligature alone, and the magnitude of systemic inflammation and aortic plaque formation were also notably greater in the mice with ligature/P.g. LPS. These observations indicate that the development of atherosclerosis is due to systemic inflammation caused by severe periodontitis. In vitro, P.g. LPS enhanced the secretion of pro-inflammatory cytokines from macrophages and increased the adhesion of monocytes to endothelial cells by upregulating the expression of adhesion molecules from endothelial cells. Moreover, secretory proteins, such as TNF-α, from macrophages induced endothelial-mesenchymal transitions of the endothelial cells. Taken together, systemic inflammation induced by severe periodontitis might exacerbate atherosclerosis via, in part, causing aberrant functions of vascular endothelial cells and the activation of macrophages in mice

Vibration Measurements of Clinched Joints

AbstractAs a result of the trend towards lightweight construction in sustainable manufacturing, there has been a significant increase in the use of clinched joints in engineering structures and components. Mechanical structures assembled by clinching are expected to possess a high damping capacity. The aim of this paper is to provide an experimental measurement technique for the investigation of the forced vibration behavior of clinched joints. The dynamic test software and the data acquisition hardware were used in the experimental measurement of the dynamic response of the clinched joints. The frequency response functions of the clinched joints of different clinching point number were measured and compared

Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

Clinical significance of serum lipids in idiopathic pulmonary alveolar proteinosis

<p>Abstract</p> <p>Background</p> <p>It is well known that pulmonary alveolar proteinosis(PAP) is characterised by accumulation of surfactant lipids and proteins within airspaces. However, few previous data describe the serum lipid levels associated with PAP.</p> <p>Materials and methods</p> <p>We retrospectively reviewed 25 patients with idiopathic PAP(iPAP). The serum lipid levels of patients with idiopathic PAP were compared with those of the healthy volunteers. In patients and healthy subjects, the LDL-C/HDL-C ratios were 2.94 ± 1.21 and 1.60 ± 0.70, respectively (<it>p </it>< 0.001), HDL-C were 1.11 ± 0.27 and 1.71 ± 0.71 respectively (<it>p </it>< 0.001). The values of LDL-C correlated significantly with those of PaO2 and P_A-aO2 (r = -0.685, <it>p </it>= 0.003, and r = 0.688, <it>p </it>= 0.003, respectively). The values of LDL-C/HDL-C ratios also correlated with PaO2 levels and PA-aO2 levels (r = -0.698, p = 0.003, and r = 0.653, p = 0.006, respectively). 11 and 13 patients experienced respectively a decline in TC and LDL-C levels following whole lung lavage(WLL), the median decline was 0.71 mmol/L(<it>p </it>< 0.009) and 0.47 mmol/L(<it>p </it>< 0.003), respectively.</p> <p>Conclusions</p> <p>the serum lipid levels, especially the levels of LDL-C and LDL-C/HDL-C, may reflect the severity of the disease in PAP patients, and predict the therapeutic effect of WLL.</p

Evidence for electron-electron interaction in topological insulator thin films

We consider in our work high quality single crystal thin films of Bi2Se3, grown by molecular beam epitaxy, both with and without Pb doping. Our ARPES data demonstrate topological surface states with a Fermi level lying inside the bulk band gap in the Pb doped filims. Transport data show weak localization behavior, as expected for a 2D system, but a detailed analysis within the standard theoretical framework of diffusive transport shows that the temperature and magnetic field dependences of resistance cannot be reconciled in a theory that neglects inter-electron interactions. We demonstrate that an excellent account of quantum corrections to conductivity is achieved when both disorder and interaction are taken into account. These results clearly demonstrate that it is crucial to include electron electron interaction for a comprehensive understanding of diffusive transport in topological insulators.Comment: Submitted to Phys. Rev.