Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

RDFa2: Lightweight semantic enrichment for hypertext content:Lightweight Semantic Enrichment for Hypertext Content

RDFa is a syntactic format that allows RDF triples to be integrated into hypertext content of HTML/XHTML documents. Although a growing number of methods or tools have been designed attempting at generating or digesting RDFa, comparatively little work has been carried out on finding a generic solution for publishing existing RDF data sets with the RDFa serialisation format. This paper proposes a generic and lightweight approach to generating semantically-enriched hypertext content by embedding RDF triples derived from diverse provenances in terms of a concept of topic nodes which will be automatically recommended by our discovery algorithm. RDFa2 is a proof-of-concept implementation for our approach and works as an online platform assisting Web content publishers in semi-automatically generating, personalising and curating pages with RDFa. RDFa2 has been introduced and employed by students in a master level course and the experimental results as well as additional case studies indicate the validity of this approach to generating triple-embedded Web documents such as online profiles and vocabularies with little user intervention.</p

Dual-mode mechanical resonance of individual ZnO nanobelts

©2003 American Institute of Physics. The electronic version of this article is the complete one and can be found online at: http://link.aip.org/link/?APPLAB/82/4806/1DOI:10.1063/1.1587878The mechanical resonance of a single ZnO nanobelt, induced by an alternative electric field, was studied by in situ transmission electron microscopy. Due to the rectangular cross section of the nanobelt, two fundamental resonance modes have been observed corresponding to two orthogonal transverse vibration directions, showing the versatile applications of nanobelts as nanocantilevers and nanoresonators. The bending modulus of the ZnO nanobelts was measured to be ~52 GPa and the damping time constant of the resonance in a vacuum of 5×10–8 Torr was ~1.2 ms and quality factor Q = 500

Exploring multipartite quantum correlations with the square of quantum discord

We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.Comment: 8 pages, 5 figure

Measurement of the mass of the τ lepton

A data-driven energy scan in the immediate vicinity of the τ pair production threshold has been performed using the Beijing Spectrometer at the Beijing Electron-Positron Collider. Approximately 5 pb^(-1) of data, distributed over 12 scan points, have been collected. A previous mass value for the τ lepton, obtained using only the eμ final state, has been published. In this paper, the final BES result on the mass measurement is presented. The analysis is based on the combined data from the ee, eμ, eh, μμ, μh, and hh final states, where h denotes a charged π or K. A maximum likelihood fit to the τ pair production cross section data yields the value m_τ=1776.96_(-0.21)-0.17^(+0.18+0.25) MeV

Spin and lattice excitations of a BiFeO3 thin film and ceramics

We present a comprehensive study of polar and magnetic excitations in BiFeO3 ceramics and a thin film epitaxially grown on an orthorhombic (110) TbScO3 substrate. Infrared reflectivity spectroscopy was performed at temperatures from 5 to 900 K for the ceramics and below room temperature for the thin film. All 13 polar phonons allowed by the factor-group analysis were observed in theceramic samples. The thin-film spectra revealed 12 phonon modes only and an additional weak excitation, probably of spin origin. On heating towards the ferroelectric phase transition near 1100 K, some phonons soften, leading to an increase in the static permittivity. In the ceramics, terahertz transmission spectra show five low-energy magnetic excitations including two which were not previously known to be infrared active; at 5 K, their frequencies are 53 and 56 cm-1. Heating induces softening of all magnetic modes. At a temperature of 5 K, applying an external magnetic field of up to 7 T irreversibly alters the intensities of some of these modes. The frequencies of the observed spin excitations provide support for the recently developed complex model of magnetic interactions in BiFeO3 (R.S. Fishman, Phys. Rev. B 87, 224419 (2013)). The simultaneous infrared and Raman activity of the spin excitations is consistent with their assignment to electromagnons