Spin-polarized currents generated by magnetic Fe atomic chains

Fe-based devices are widely used in spintronics because of high spin-polarization and magnetism. In this work, free-standing Fe atomic chains were proposed to be used as the thinnest wires to generate spin-polarized currents due to the spin-polarized energy bands. By ab initio calculations, the zigzag structure was found more stable than the wide-angle zigzag structure and has higher ratio of spin-up and spin-down currents. By our theoretical prediction, Fe atomic chains have sufficiently long thermal lifetime only at T<=150 K, while C atomic chains are very stable even at T=1000 K. This result means that the spintronic devices based on Fe chains could only work at low temperature. A system constructed by a short Fe chain sandwiched between two graphene electrodes was proposed as a spin-polarized current generator, while a C chain does not have such property. The present work may be instructive and meaningful to further practical applications based on recent technical development on the preparation of metal atomic chains [Proc. Natl. Acad. Sci. U.S.A. 107, 9055 (2010)].Comment: Nanotechnology (2014

On Degrees of Freedom of Projection Estimators with Applications to Multivariate Nonparametric Regression

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as outputs of linearly constrained quadratic optimization procedures, namely, minimizers of the least squares criterion with linear constraints and/or quadratic penalties. As special cases of our results, we derive explicit expressions for the degrees of freedom in many nonparametric regression problems, e.g., bounded isotonic regression, multivariate (penalized) convex regression, and additive total variation regularization. Our theory also yields, as special cases, known results on the degrees of freedom of many well-studied estimators in the statistics literature, such as ridge regression, Lasso and generalized Lasso. Our results can be readily used to choose the tuning parameter(s) involved in the estimation procedure by minimizing the Stein's unbiased risk estimate. As a by-product of our analysis we derive an interesting connection between bounded isotonic regression and isotonic regression on a general partially ordered set, which is of independent interest.Comment: 72 pages, 7 figures, Journal of the American Statistical Association (Theory and Methods), 201

Community Detection by L0L_0-penalized Graph Laplacian

Community detection in network analysis aims at partitioning nodes in a network into $K$ disjoint communities. Most currently available algorithms assume that $K$ is known, but choosing a correct $K$ is generally very difficult for real networks. In addition, many real networks contain outlier nodes not belonging to any community, but currently very few algorithm can handle networks with outliers. In this paper, we propose a novel model free tightness criterion and an efficient algorithm to maximize this criterion for community detection. This tightness criterion is closely related with the graph Laplacian with $L_0$ penalty. Unlike most community detection methods, our method does not require a known $K$ and can properly detect communities in networks with outliers. Both theoretical and numerical properties of the method are analyzed. The theoretical result guarantees that, under the degree corrected stochastic block model, even for networks with outliers, the maximizer of the tightness criterion can extract communities with small misclassification rates even when the number of communities grows to infinity as the network size grows. Simulation study shows that the proposed method can recover true communities more accurately than other methods. Applications to a college football data and a yeast protein-protein interaction data also reveal that the proposed method performs significantly better.Comment: 40 pages, 15 Postscript figure

Galaxy formation with cold gas accretion and evolving stellar initial mass function

The evolution of the galaxy stellar mass function is especially useful to test the current model of galaxy formation. Observational data have revealed a few inconsistencies with predictions from the $\Lambda {\rm CDM}$ model. For example, most massive galaxies have already been observed at very high redshifts, and they have experienced only mild evolution since then. In conflict with this, semi-analytical models of galaxy formation predict an insufficient number of massive galaxies at high redshift and a rapid evolution between redshift 1 and 0 . In addition, there is a strong correlation between star formation rate and stellar mass for star-forming galaxies, which can be roughly reproduced with the model, but with a normalization that is too low at high redshift. Furthermore, the stellar mass density obtained from the integral of the cosmic star formation history is higher than the measured one by a factor of 2. In this paper, we study these issues using a semi-analytical model that includes: 1) cold gas accretion in massive halos at high redshift; 2) tidal stripping of stellar mass from satellite galaxies; and 3) an evolving stellar initial mass function (bottom-light) with a higher gas recycle fraction. Our results show that the combined effects from 1) and 2) can predict sufficiently massive galaxies at high redshifts and reproduce their mild evolution at low redshift, While the combined effects of 1) and 3) can reproduce the correlation between star formation rate and stellar mass for star-forming galaxies across wide range of redshifts. A bottom-light/top-heavy stellar IMF could partly resolve the conflict between the stellar mass density and cosmic star formation history.Comment: 9 pages, 7 figures. Accepted for publication in Ap

Predicting the chemical stability of monatomic chains

A simple model for evaluating the thermal atomic transfer rates in nanosystems [EPL 94, 40002 (2011)] was developed to predict the chemical reaction rates of nanosystems with small gas molecules. The accuracy of the model was verified by MD simulations for molecular adsorption and desorption on a monatomic chain. By the prediction, a monatomic carbon chain should survive for 120 years in the ambient of 1 atm O2 at room temperature, and it is very invulnerable to N2, H2O, NO2, CO and CO2, while a monatomic gold chain quickly ruptures in vacuum. It is worth noting that since the model can be easily applied via common ab initio calculations, it could be widely used in the prediction of chemical stability of nanosystems