Smooth Adjustment for Correlated Effects

This paper considers a high dimensional linear regression model with corrected variables. A variety of methods have been developed in recent years, yet it is still challenging to keep accurate estimation when there are complex correlation structures among predictors and the response. We propose an adaptive and "reversed" penalty for regularization to solve this problem. This penalty doesn't shrink variables but focuses on removing the shrinkage bias and encouraging grouping effect. Combining the l_1 penalty and the Minimax Concave Penalty (MCP), we propose two methods called Smooth Adjustment for Correlated Effects (SACE) and Generalized Smooth Adjustment for Correlated Effects (GSACE). Compared with the traditional adaptive estimator, the proposed methods have less influence from the initial estimator and can reduce the false negatives of the initial estimation. The proposed methods can be seen as linear functions of the new penalty's tuning parameter, and are shown to estimate the coefficients accurately in both extremely highly correlated variables situation and weakly correlated variables situation. Under mild regularity conditions we prove that the methods satisfy certain oracle property. We show by simulations and applications that the proposed methods often outperforms other methods

Meromorphic differentials with twisted coefficients on compact Riemann surfaces

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the existence of differentials with twisted coefficients of the second and third kinds under a suitable assumption on residues.Comment: 20 page

Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical Lasso Estimator (SLS-GLE). The procedure uses the estimated precision matrix to describe the specific information on the conditional dependence pattern among predictors, and encourages both sparsity on the regression model and the graphical model. We introduce the Laplacian quadratic penalty adopting the graph information, and give detailed discussions on the advantages of using the precision matrix to construct the Laplacian matrix. Theoretical properties and numerical comparisons are presented to show that the proposed method improves both model interpretability and accuracy of estimation. We also apply this method to a financial problem and prove that the proposed procedure is successful in assets selection

Computational multiheterodyne spectroscopy

Dual comb spectroscopy allows for high-resolution spectra to be measured over broad bandwidths, but an essential requirement for coherent integration is the availability of a phase reference. Usually, this means that the combs' phase and timing errors must be measured and either minimized by stabilization or removed by correction, limiting the technique's applicability. In this work, we demonstrate that it is possible to extract the phase and timing signals of a multiheterodyne spectrum completely computationally, without any extra measurements or optical elements. These techniques are viable even when the relative linewidth exceeds the repetition rate difference, and can tremendously simplify any dual comb system. By reconceptualizing frequency combs in terms of the temporal structure of their phase noise, not their frequency stability, we are able to greatly expand the scope of multiheterodyne techniques

First-principles study of two-dimensional van der Waals heterojunctions

Research on graphene and other two-dimensional (2D) materials, such as silicene, germanene, phosphorene, hexagonal boron nitride (h-BN), graphitic carbon nitride (g-C3N4), graphitic zinc oxide (g-ZnO) and molybdenum disulphide (MoS2), has recently received considerable interest owing to their outstanding properties and wide applications. Looking beyond this field, combining the electronic structures of 2D materials in ultrathin van der Waals heterojunctions has also emerged to widely study theoretically and experimentally to explore some new properties and potential applications beyond their single components. Here, this article reviews our recent theoretical studies on the structural, electronic, electrical and optical properties of 2D van der Waals heterojunctions using density functional theory calculations, including the Graphene/Silicene, Graphene/Phosphorene, Graphene/g-ZnO, Graphene/MoS2 and g-C3N4/MoS2 heterojunctions. Our theoretical simulations, designs and calculations show that novel 2D van der Waals heterojunctions provide a promising future for electronic, electrochemical, photovoltaic, photoresponsive and memory devices in the experiments.Comment: 12 pages, 5 figures in Computational Materials Science (2015). arXiv admin note: text overlap with arXiv:1411.035

Learning Belief Networks in Domains with Recursively Embedded Pseudo Independent Submodels

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a single link search. Earlier work on learning PI models has suggested a straightforward multi-link search algorithm. However, when a domain contains recursively embedded PI submodels, it may escape the detection of such an algorithm. In this paper, we propose an improved algorithm that ensures the learning of all embedded PI submodels whose sizes are upper bounded by a predetermined parameter. We show that this improved learning capability only increases the complexity slightly beyond that of the previous algorithm. The performance of the new algorithm is demonstrated through experiment.Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997

Effects of Pressure on the Electronic Structures of LaOFeP

We studied the electronic structures of LaOFeP under applied pressure using first-principles calculations. The electronic density of states at the Fermi level decreases continuously with increasing pressure. The electron branches of Fermi surfaces are rather robust to pressure, while the hole branches change significantly. Two hole surfaces shrink into small ellipsoid-like surfaces and disappear finally, at which the applied pressure is ~ 74.7 GPa. The pressure response can be understood by the band structures around the Fermi level. Comparative studies reveal that the disappearance of hole surfaces is mainly due to the compression of the FeP layer along the c-axis of unit cell.Comment: 26 pages, 9 figure

Semi-continuity for total dimension divisors of \'etale sheaves

In this article, we extend a pull-back inequality for total dimension divisors of \'etale sheavs due to Saito. Using this formula, we generalize Deligne and Laumon's lower semi-continuous property for Swan conductors of \'etale sheaves on relative curves to higher relative dimensions in a geometric situation.Comment: 16 pages. Improve the writing in the new versio

Weierstrass Semigroups from Kummer Extensions

The Weierstrass semigroups and pure gaps can be helpful in constructing codes with better parameters. In this paper, we investigate explicitly the minimal generating set of the Weierstrass semigroups associated with several totally ramified places over arbitrary Kummer extensions. Applying the techniques provided by Matthews in her previous work, we extend the results of specific Kummer extensions studied in the literature. Some examples are included to illustrate our results.Comment: 12 page

Defect in Phosphorene

Defects are inevitably present in materials and always can affect their properties. Here, first-principles calculations are performed to systematically study the stability, structural and electronic properties of ten kinds of point defects in semiconducting phosphorene, including the Stone-Wales (SW-1 and SW-2) defect, single (SV59 and SV5566) and double vacancy (DV585-1, DV585-2, DV555777-1, DV555777-2, DV555777-3 and DV4104) defects. We find that these defects are all much easily created in phosphorene with higher areal density compared with graphene and silicene. They are easy distinguish each other and correlate with their defective atomic structures with simulated scanning tunneling microscopy images at positive bias. The SW, DV585-1, DV555777 and DV4104 defects have little effect on phosphorene's electronic properties and defective phosphorene monolayers still show semiconducting with similar band gap values to perfect phosphorene. The SV59 and DV585-2 defects can introduce unoccupied localized states into phosphorene's fundamental band gap. Specifically, the SV59 and 5566 defects can induce hole doping in phosphorene, and only the stable SV59 defect can result in local magnetic moments in phosphorene different from all other defects.Comment: 5 pages, 4 figure