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

Tick-borne encephalitis virus induces chemokine RANTES expression via activation of IRF-3 pathway.

BACKGROUND: Tick-borne encephalitis virus (TBEV) is one of the most important flaviviruses that targets the central nervous system (CNS) and causes encephalitides in humans. Although neuroinflammatory mechanisms may contribute to brain tissue destruction, the induction pathways and potential roles of specific chemokines in TBEV-mediated neurological disease are poorly understood. METHODS: BALB/c mice were intracerebrally injected with TBEV, followed by evaluation of chemokine and cytokine profiles using protein array analysis. The virus-infected mice were treated with the CC chemokine antagonist Met-RANTES or anti-RANTES mAb to determine the role of RANTES in affecting TBEV-induced neurological disease. The underlying signaling mechanisms were delineated using RANTES promoter luciferase reporter assay, siRNA-mediated knockdown, and pharmacological inhibitors in human brain-derived cell culture models. RESULTS: In a mouse model, pathological features including marked inflammatory cell infiltrates were observed in brain sections, which correlated with a robust up-regulation of RANTES within the brain but not in peripheral tissues and sera. Antagonizing RANTES within CNS extended the survival of mice and reduced accumulation of infiltrating cells in the brain after TBEV infection. Through in vitro studies, we show that virus infection up-regulated RANTES production at both mRNA and protein levels in human brain-derived cell lines and primary progenitor-derived astrocytes. Furthermore, IRF-3 pathway appeared to be essential for TBEV-induced RANTES production. Site mutation of an IRF-3-binding motif abrogated the RANTES promoter activity in virus-infected brain cells. Moreover, IRF-3 was activated upon TBEV infection as evidenced by phosphorylation of TBK1 and IRF-3, while blockade of IRF-3 activation drastically reduced virus-induced RANTES expression. CONCLUSIONS: Our findings together provide insights into the molecular mechanism underlying RANTES production induced by TBEV, highlighting its potential importance in the process of neuroinflammatory responses to TBEV infection

miRNAs-mediated overexpression of Periostin is correlated with poor prognosis and immune infiltration in lung squamous cell carcinoma.

Lung cancer is one of the most common malignancies with a high mortality rate worldwide. POSTN has been shown to be strongly correlated with the poor prognosis of lung cancer patients. However, the function and mechanism of action of POSTN in lung cancer remain unclear. Here, we carried out a pan-cancer analysis to assess the clinical prognostic value of POSTN based on the TCGA, TIMER, Oncomine, Kaplan-Meier, and UALCAN databases. We found that upregulated POSTN can be a promising biomarker to predict the prognosis of patients with lung cancer. High levels of POSTN correlated with immune cell infiltration in lung cancer, especially lung squamous cell carcinoma (LUSC), which was further confirmed based on the results from the TISIDB database. Moreover, the expression analysis, correlation analysis, and survival analysis revealed that POSTN-targeted miRNAs, downregulation of has-miR-144-3p and has-miR-30e-3p, were significantly linked to poor prognosis in patients with LUSC. Taken together, we identified that POSTN can act as a novel biomarker for determining the prognosis related to immune infiltration in patients with LUSC and deserves further research

Existence problem of proton semi-bubble structure in the 21+2_1^+ state of 34^{34}Si

The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si. The experimental excitation energy and the B(E2) strength of the $2_1^+$ state in $^{34}$Si can be reproduced quite well. The tensor effect is also studied. It is shown that the tensor interaction has a notable impact on the excitation energy of the $2_1^+$ state and a small effect on the B(E2) value. Besides, its effect on the density distributions in the ground and $2_1^+$ state of $^{34}$Si is negligible. Our present results with T36 and T44 show that the $2_1^+$ state of $^{34}$Si is mainly caused by proton transiton from $\pi 1d_{5/2}$ orbit to $\pi 2s_{1/2}$ orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.Comment: 6 pages, 3 figures, 3 table

A Population of Radio-loud Narrow Line Seyfert 1 Galaxies with Blazar-like Properties?

(abridged) We present a comprehensive study of a sample of 23 genuine radio-loud NLS1 galaxies which have the radio-loudness parameters greater than 100. The radio sources of the sample are ubiquitously compact. A significant fraction of these objects show interesting radio to X-ray properties that are unusual to most of the previously known radio-loud NLS1 AGN, but are reminiscent of blazars. These include flat radio spectra, large amplitude flux and spectral variability, compact VLBI cores, very high brightness temperatures derived from variability, enhanced optical emission in excess of the normal ionising continuum, flat X-ray spectra, and blazar-like SEDs. We interpret them as evidence for the postulated blazar nature of these very radio-loud NLS1 AGN, which might possess at least moderately relativistic jets. Intrinsically, some of the objects have relatively low radio power and would have been classified as radio-intermediate AGN. The black hole masses are estimated to be within 10^{6-8}Msun, and the inferred Eddington ratios are around unity. The results imply that radio-loud AGN may be powered by black holes with moderate masses (10^{6-7}Msun) accreting at high rates. We find that a significant fraction of the objects, despite having strong emission lines, resemble high-energy peaked BL Lacs (HBL) in their SED. Given the peculiarities of blazar-like NLS1 galaxies, questions arise as to whether they are plain downsizing extensions of normal radio-loud AGN, or whether they form a previously unrecognised population.Comment: Comments: 29 pages, 16 figures, 4 tables, accepted for publication in Ap