Optimal rates of convergence for covariance matrix estimation

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm. It is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation. The minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties. A key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound. The technical analysis requires new ideas that are quite different from those used in the more conventional function/sequence estimation problems.Comment: Published in at http://dx.doi.org/10.1214/09-AOS752 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Valence bond spin liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets

Fermionic valence bond approach in terms of SU(4) representation is proposed to describe the $J_{1}-J_{2}$ frustrated Heisenberg antiferromagnetic (AF) model on a {\it bipartite} square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence bond spin liquid state, interpolating the two different AF ordered states in the large $J_{1}$ and large $J_{2}$ limits, respectively. This novel spin liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta ${\bf q}=(0,0)$ and $(\pi ,\pi)$ in the strongly frustrated limit $J_{2}/J_{1}\sim 1/2$, which can be checked by neutron scattering experiment.Comment: Revtex file, 4 pages, 4 figure

Dispersive Coupling Between the Superconducting Transmission Line Resonator and the Double Quantum Dots

Realization of controllable interaction between distant qubits is one of the major problems in scalable solid state quantum computing. We study a superconducting transmission line resonator (TLR) as a tunable dispersive coupler for the double-dot molecules. A general interaction Hamiltonian of $n$ two-electron spin-based qubits and the TLR is presented, where the double-dot qubits are biased at the large detuning region and the TLR is always empty and virtually excited. Our analysis o the main decoherence sources indicates that various major quantum operations can be reliably implemented with current technology.Comment: 10 pages, 5 figure

Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions

High precision multipole polarizabilities, $\alpha_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H and H-He$^+$ interactions are given.Comment: 8 figures, 8 table

Positivity constraints on LECs of χ\chiPT lagrangian at \cO(p^6) level

Positivity constraints on the LECs of \cO(p^6) $\chi$PT lagrangian are discussed. We demonstrate that the constraints are automatically satisfied inside the Mandelstam triangle for $\pi\pi$ scatterings, when $N_C$ is large. Numerical tests are made in the $N_C=3$ case, and it is found that these constraints are also well respected.Comment: 9 pages with 2 eps figure

Consumer-Led Screening for Atrial Fibrillation:A Report From the mAFA-II Trial Long-Term Extension Cohort

BACKGROUND: There are limited data on mobile health detection of prevalent atrial fibrillation (AF) and its related risk factors over time. OBJECTIVES: This study aimed to report the trends on prevalent AF detection over time and risk factors, with a consumer-led photoplethysmography screening approach. METHODS: 3,499,461 subjects aged over 18 years, who use smart devices (Huawei Technologies Co.) were enrolled between October 26, 2018, and December 1, 2021. RESULTS: Among 2,852,217 subjects for AF screening, 12,244 subjects (0.43%; 83.2% male, mean age 57 ± 15 years) detected AF episodes. When compared with 2018, the risk (adjusted HRs, 95% CI) for monitored prevalent AF increased significantly for subjects when monitoring started in 2020 (adjusted HR: 1.34; 95% CI: 1.27-1.40; P 93% confirmation of detected AF episodes even for the low-risk general population, highlighting the increased risk for detecting prevalent AF and the need for modification of OSA that increase AF susceptibility. (Mobile Health [mHealth] Technology for Improved Screening, Patient Involvement and Optimizing Integrated Care in Atrial Fibrillation [mAFA (mAF-App) II study]; ChiCTR-OOC-17014138