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

Sizing energy storage on the 11kV distribution network

The cost and limited flexibility of traditional approaches to 11kV network reinforcement threatens to constrain the uptake of low carbon technologies. Ofgem has released £500m of funding for DNOs to trial innovative techniques and share the learning with the rest of the industry. One of the techniques under study is the addition of Energy Storage at key substations to the network to help with peak load lopping. This paper looks in detail at the sizing algorithm for use in the assessment of alternatives to traditional reinforcement and investigates a method of sizing a battery for use on a Network taking into account load growth, capacity fade and battery lifecycle issues. A further complication to the analysis is the method of operation of the battery system and how this affects the Depth of Discharge (DoD). The proposed method is being trialled on an area of 11kV network in Milton Keynes Central area and the simulation results are presented in this paper

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

Expression of human soluble tumor necrosis factor (TNF)-related apoptosis-inducing ligand in transplastomic tobacco

The soluble extracellular domain of tumor necrosis factor (TNF)-related apoptosis-inducing ligand (sTRAIL) can, as the whole length TRAIL protein, bind with its receptors and specifically induce the apoptosis of cancer cells; therefore, it has been developed as a potential therapeutic agent for various cancer treatments. As it has become an attractive technology for foreign protein production, especially for production of biopharmaceuticals, chloroplast engineering was applied in this study to express human sTRAIL protein in tobacco. Two transplastomic lines were obtained. Southern blot showed that sTRAIL gene was inserted into the right site of the tobacco chloroplast genome. RT-PCR results also confirmed that the foreign gene is transcribed in both lines. However, western blot showed that only one line accumulated sTRAIL protein stably, while the other line lost the ability to accumulate this protein after several rounds of subcultures. The possible reason for this unexpected phenomenon is discussed.Key words: Chloroplast transformation, sTRAIL, pharmaceutical protein, expression, tobacco chloroplast

Retinal image enhancement via a multiscale morphological approach with OCCO filter.

Retinal images are widely used for diagnosis and eye disease detection. However, due to the acquisition process, retinal images often have problems such as low contrast, blurry details or artifacts. These problems may severely affect the diagnosis. Therefore, it is very impor tant to enhance the visual quality of such images. Contrast enhancement is a pre-processing applied to images to improve their visual quality. This technique betters the identification of retinal structures in degraded reti nal images. In this work, a novel algorithm based on multi-scale mathe matical morphology is presented. First, the original image is blurred us ing the Open-Close Close-Open (OCCO) filter to reduce any artifacts in the image. Next, multiple bright and dark features are extracted from the filtered image by the Top-Hat transform. Finally, the maximum bright values are added to the original image and the maximum dark values are subtracted from the original image, previously adjusted by a weight. The algorithm was tested on 397 retinal images from the public STARE database. The proposed algorithm was compared with state of the art al gorithms and results show that the proposal is more efficient in improving contrast, maintaining similarity with the original image and introducing less distortion than the other algorithms. According to ophthalmologists, the algorithm, by improving retinal images, provides greater clarity in the blood vessels of the retina and would facilitate the identification of pathologies.CONACYT - Consejo Nacional de Ciencia y TecnologíaPROCIENCI

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