A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true $s$-sparse precision matrix under the spectral norm is $s\sqrt{\log p/n}$ when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise $L_{\infty}$ norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implementable by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.Comment: To appear in Journal of the American Statistical Associatio

Thresholdless dressed-atom laser in a photonic band-gap material

We demonstrate the capability of complete thresholdless lasing operation between dressed states of a two-level atom located inside a microscopic cavity engineered in a photonic band-gap material. We distinguish between threshold and thresholdless behaves by analyzing the Mandel's Q parameter for the cavity field. We find that the threshold behave depends on whether the spontaneous emission is or is not present on the lasing transition. In the presence of the spontaneous emission, the mean photon number of the cavity field exhibits threshold behavior indicating that the system may operate as an ordinary laser. When the spontaneous emission is eliminated on the lasing transition, no threshold is observed for all values of the pumping rate indicating the system becomes a thresholdless laser. Moreover, we find that under a thresholdless operation, the mean photon number can increase nonlinearly with the pumping rate, and this process is accompanied by a sub-Poisson statistics of the field. This suggests that the nonclassical statistics can be used to distinguish a nonlinear operation of the dressed-atom laser.Comment: 6 pages 4 figure

Extended dual description of Mott transition beyond two-dimensional space

Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.Comment: 7 pages, no figure

Bound States and Critical Behavior of the Yukawa Potential

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp(-\alpha r)/ r$, using different algorithms: solving the Schr\"odinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $\alpha=\alpha_C$, above which no bound state exists. We study the relation between $\alpha_C$ and $\lambda$ for various angular momentum quantum number $l$, and find in atomic units, $\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in China

Single-electron latch with granular film charge leakage suppressor

A single-electron latch is a device that can be used as a building block for Quantum-dot Cellular Automata (QCA) circuits. It consists of three nanoscale metal "dots" connected in series by tunnel junctions; charging of the dots is controlled by three electrostatic gates. One very important feature of a single-electron latch is its ability to store ("latch") information represented by the location of a single electron within the three dots. To obtain latching, the undesired leakage of charge during the retention time must be suppressed. Previously, to achieve this goal, multiple tunnel junctions were used to connect the three dots. However, this method of charge leakage suppression requires an additional compensation of the background charges affecting each parasitic dot in the array of junctions. We report a single-electron latch where a granular metal film is used to fabricate the middle dot in the latch which concurrently acts as a charge leakage suppressor. This latch has no parasitic dots, therefore the background charge compensation procedure is greatly simplified. We discuss the origins of charge leakage suppression and possible applications of granular metal dots for various single-electron circuits.Comment: 21 pages, 4 figure

Analysis of electromagnetic interference from power system processing and transmission components for Space Station Freedom

The goal is to analyze the potential effects of electromagnetic interference (EMI) originating from power system processing and transmission components for Space Station Freedom.The approach consists of four steps: (1) develop analytical tools (models and computer programs); (2) conduct parameterization studies; (3) predict the global space station EMI environment; and (4) provide a basis for modification of EMI standards

Estimating correlation between multivariate longitudinal data in the presence of heterogeneity

Abstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linear mixed model (BLMM) provides a versatile tool with regard to assessing correlation. However, BLMMs often assume that all individuals are drawn from a single homogenous population where the individual trajectories are distributed smoothly around population average. Methods Using longitudinal mean deviation (MD) and visual acuity (VA) from the Ocular Hypertension Treatment Study (OHTS), we demonstrated strategies to better understand the correlation between multivariate longitudinal data in the presence of potential heterogeneity. Conditional correlation (i.e., marginal correlation given random effects) was calculated to describe how the association between longitudinal outcomes evolved over time within specific subpopulation. The impact of heterogeneity on correlation was also assessed by simulated data. Results There was a significant positive correlation in both random intercepts (ρ = 0.278, 95% CI: 0.121–0.420) and random slopes (ρ = 0.579, 95% CI: 0.349–0.810) between longitudinal MD and VA, and the strength of correlation constantly increased over time. However, conditional correlation and simulation studies revealed that the correlation was induced primarily by participants with rapid deteriorating MD who only accounted for a small fraction of total samples. Conclusion Conditional correlation given random effects provides a robust estimate to describe the correlation between multivariate longitudinal data in the presence of unobserved heterogeneity (NCT00000125)