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

Myocardial fibrosis in stroke survivors

Stroke survivors are most likely to die of cardiac death, yet few undergo comprehensive cardiac assessment to look for reversible causes. Myocardial fibrosis (MF) is not only the hallmark of cardiomyopathy, but also a substrate for sudden cardiac death, ventricular tachyarrhythmia and heart failure. Procollagen carboxyl-terminal telopeptide (PICP) was found to be a marker of MF. The relationship between PICP and cardiac abnormalities in stroke survivors is unknown. We recently showed that MF in stroke survivors can be treated by spironolactone and amiloride in a randomised placebo-controlled cross-over study with reduction in PICP levels and QTc [1]

Ignition characterization of LOX/hydrocarbon propellants

The results of an evaluation of the ignition characteristics of the gaseous oxygen (Gox)/Ethanol propellant combination are presented. Ignition characterization was accomplished through the analysis, design, fabrication and testing of a spark initiated torch igniter and prototype 620 lbF thruster/igniter assembly. The igniter was tested over a chamber pressure range of 74 to 197 psia and mixture ratio range of 0.778 to 3.29. Cold (-92 to -165 F) and ambient (44 to 80 F) propellant temperatures were used. Spark igniter ignition limits and thruster steady state and pulse mode, performance, cooling and stability data are presented. Spark igniter ignition limits are presented in terms of cold flow pressure, ignition chamber diameter and mixture ratio. Thruster performance is presented in terms of vacuum specific impulse versus engine mixture ratio. Gox/Ethanol propellants were shown to be ignitable over a wide range of mixture ratios. Cold propellants were shown to have a minor effect on igniter ignition limits. Thruster pulse mode capability was demonstrated with multiple pulses of 0.08 sec duration and less

Models of Financial Markets with Extensive Participation Incentives

We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive-sumness of the players' wealths provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market-makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data.Comment: 17 pages, 16 figure

Heavy flavor kinetics at the hadronization transition

We investigate the in-medium modification of the charmonium breakup processes due to the Mott effect for light (pi, rho) and open-charm (D, D*) quark-antiquark bound states at the chiral/deconfinement phase transition. The Mott effect for the D-mesons effectively reduces the threshold for charmonium breakup cross sections, which is suggested as an explanation of the anomalous J/psi suppression phenomenon in the NA50 experiment. Further implications of finite-temperature mesonic correlations for the hadronization of heavy flavors in heavy-ion collisions are discussed.Comment: 4 pages, 2 figures, Contribution to SQM2001 Conference, submitted to J. Phys.

Oscillatory Spin Polarization and Magneto-Optic Kerr Effect in Fe3O4 Thin Films on GaAs(001)

The spin dependent properties of epitaxial Fe3O4 thin films on GaAs(001) are studied by the ferromagnetic proximity polarization (FPP) effect and magneto-optic Kerr effect (MOKE). Both FPP and MOKE show oscillations with respect to Fe3O4 film thickness, and the oscillations are large enough to induce repeated sign reversals. We attribute the oscillatory behavior to spin-polarized quantum well states forming in the Fe3O4 film. Quantum confinement of the t2g states near the Fermi level provides an explanation for the similar thickness dependences of the FPP and MOKE oscillations.Comment: to appear in Phys. Rev. Let

Capacity Analysis of Interference Alignment With Bounded CSI Uncertainty

Interference alignment (IA) has been demonstrated to achieve the degree-of-freedom (DoF) of an interference channel given perfect global channel state information (CSI). In this letter, we consider the case of imperfect CSI with bounded errors and derive a capacity lower bound of the channel using IA. We show that this lower bound is within 1 bps/Hz of the capacity of the perfect CSI case up to a certain signal-to-noise ratio (SNR) which we refer to it as the saturating SNR. Further, we introduce a new metric called modified DoF (mDoF) in order to characterize the multiplexing performance of IA with imperfect CSI at finite SNR. Simulation results for the 3-user case are provided to illustrate the region within which the actual capacity of IA falls

Coherent transport in Nb/delta-doped-GaAs hybrid microstructures

Coherent transport in Nb/GaAs superconductor-semiconductor microstructures is presented. The structures fabrication procedure is based on delta-doped layers grown by molecular-beam-epitaxy near the GaAs surface, followed by an As cap layer to protect the active semiconductor layers during ex situ transfer. The superconductor is then sputter deposited in situ after thermal desorption of the protective layer. Two types of structures in particular will be discussed, i.e., a reference junction and the engineered one that contains an additional insulating AlGaAs barrier inserted during the growth in the semiconductor. This latter configuration may give rise to controlled interference effects and realizes the model introduced by de Gennes and Saint-James in 1963. While both structures show reflectionless tunneling-dominated transport, only the engineered junction shows additionally a low-temperature single marked resonance peaks superimposed to the characteristic Andreev-dominated subgap conductance. The analysis of coherent magnetotransport in both microstructures is successfully performed within the random matrix theory of Andreev transport and ballistic effects are included by directly solving the Bogoliubov-de Gennes equations. The impact of junction morphology on reflectionless tunneling and the application of the employed fabrication technique to the realization of complex semiconductor-superconductor systems are furthermore discussed.Comment: 9 pages, 8 figures, invited review paper, to be published in Mod. Phys. Lett.