Asymptotic Laplacian-Energy-Like Invariant of Lattices

Let $\mu_1\ge \mu_2\ge\cdots\ge\mu_n$ denote the Laplacian eigenvalues of $G$ with $n$ vertices. The Laplacian-energy-like invariant, denoted by $LEL(G)= \sum_{i=1}^{n-1}\sqrt{\mu_i}$, is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.Comment: 6 pages, 2 figure

Misclassification Errors and the Underestimation of U.S. Unemployment Rates

Using recent results in the measurement error literature, we show that the official U.S. unemployment rates substantially underestimate the true levels of unemployment, due to misclassification errors in labor force status in Current Population Surveys. Our closed-form identification of the misclassification probabilities relies on the key assumptions that the misreporting behaviors only depend on the true values and that the true labor force status dynamics satisfy a Markov-type property. During the period of 1996 to 2009, the corrected monthly unemployment rates are 1 to 4.6 percentage points (25% to 45%) higher than the official rates, and are more sensitive to changes in business cycles. Labor force participation rates, however, are not affected by this correction. We also provide results for various subgroups of the U.S. population defined by gender, race and age.unemployment rate, labor force participation rate, misclassification, measurement error, Current Population Survey

Computational Study of the Magnetic Structure of Na2_2IrO3_3

The magnetic structure of honeycomb iridate Na$_2$IrO$_3$ is of paramount importance to its exotic properties. The magnetic order is established experimentally to be zigzag antiferromagnetic. However, the previous assignment of ordered moment to the $\bm{a}$-axis is tentative. We examine the magnetic structure of Na$_{2}$IrO$_{3}$ using first-principles methods. Our calculations reveal that total energy is minimized when the zigzag antiferromagnetic order is magnetized along $\bm{g}\approx\bm{a}+\bm{c}$. Such a magnetic configuration is explained by adding anisotropic interactions to the nearest-neighbor Kitaev-Heisenberg model. Spin-wave spectrum is also calculated, where the calculated spin gap of $10.4$ meV can in principle be measured by future inelastic neutron scattering experiments. Finally we emphasize that our proposal is consistent with all known experimental evidence, including the most relevant resonant x-ray magnetic scattering measurements [X. Liu \emph{et al.} {Phys. Rev. B} \textbf{83}, 220403(R) (2011)].Comment: 18 pages, 7 figure