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

Impurity scattering and Friedel oscillations in mono-layer black phosphorus

We study the effect of impurity scattering effect in black phosphorurene (BP) in this work. For single impurity, we calculate impurity induced local density of states (LDOS) in momentum space numerically based on tight-binding Hamiltonian. In real space, we calculate LDOS and Friedel oscillation analytically. LDOS shows strong anisotropy in BP. Many impurities in BP are investigated using $T$-matrix approximation when the density is low. Midgap states appear in band gap with peaks in DOS. The peaks of midgap states are dependent on impurity potential. For finite positive potential, the impurity tends to bind negative charge carriers and vise versa. The infinite impurity potential problem is related to chiral symmetry in BP

Heterodimerization of apelin receptor and neurotensin receptor 1 induces phosphorylation of ERK1/2 and cell proliferation via Gαq-mediated mechanism

Dimerization of G protein-coupled receptors (GPCRs) is crucial for receptor function including agonist affinity, efficacy, trafficking and specificity of signal transduction, including G protein coupling. Emerging data suggest that the cardiovascular system is the main target of apelin, which exerts an overall neuroprotective role, and is a positive regulator of angiotensin-converting enzyme 2 (ACE2) in heart failure. Moreover, ACE2 cleaves off C-terminal residues of vasoactive peptides including apelin-13, and neurotensin that activate the apelin receptor (APJ) and neurotensin receptor 1 (NTSR1) respectively, that belong to the A class of GPCRs. Therefore, based on the similar mode of modification by ACE2 at peptide level, the homology at amino acid level and the capability of forming dimers with other GPCRs, we have been suggested that APJ and NTSR1 can form a functional heterodimer. Using co-immunoprecipitation, BRET and FRET, we provided conclusive evidence of heterodimerization between APJ and NTSR1 in a constitutive and induced form. Upon agonist stimulation, hetrodimerization enhanced ERK1/2 activation and increased proliferation via activation of Gq α-subunits. These novel data provide evidence for a physiological role of APJ/NTSR1 heterodimers in terms of ERK1/2 activation and increased intracellular calcium and induced cell proliferation and provide potential new pharmaceutical targets for cardiovascular disease. © 2014 The Authors

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