arXiv subjects
Publications and source records attributed to Ao Zhang.
This letter is about effective approximation for a stochastic parabolic equation with a large potential in a periodic medium. Under a condition on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a solution of an effective equation.
We investigate the spin-valley polarization in MoTe$_2$ monolayer on (111) and (001) surfaces of ferromagnetic semiconductor EuO based on first-principles calculations. We consider surface reconstructions for EuO(111). We find that there is no direct chemical bonding between the reconstructed EuO(111) and the MoTe$_2$ overlayer, in contrast to the case of the ideal EuO(111). However, there is a strong hybridization between the states of MoTe$_2$ and the substrate states, which has a substantial impact on the valleys. The valley polarization due to the magnetic proximity effect is dependent on the detail of the interface structure, which is in the range of a few meV to about 40 meV. These values are at least one order of magnitude smaller than that induced by the ideal EuO(111). When the MoTe$_2$ monolayer is interfaced with EuO(001), the valley polarization is about 3.2 meV, insensitive to the interface structure. By a low-energy effective Hamiltonian model, the effective Zeeman field induced by EuO(001) is about 27 T, comparable to that for WSe$_2$/EuS obtained by experiment.
Graph neural networks (GNNs) achieve remarkable performance for tasks on graph data. However, recent works show they are extremely vulnerable to adversarial structural perturbations, making their outcomes unreliable. In this paper, we propose DefenseVGAE, a novel framework leveraging variational graph autoencoders(VGAEs) to defend GNNs against such attacks. DefenseVGAE is trained to reconstruct graph structure. The reconstructed adjacency matrix can reduce the effects of adversarial perturbations and boost the performance of GCNs when facing adversarial attacks. Our experiments on a number of datasets show the effectiveness of the proposed method under various threat models. Under some settings it outperforms existing defense strategies. Our code has been made publicly available at https://github.com/zhangao520/defense-vgae.
We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of an effective equation. Our method is based on two-scale convergence and Bloch waves theory.
Learning a classifier with control on the false-positive rate plays a critical role in many machine learning applications. Existing approaches either introduce prior knowledge dependent label cost or tune parameters based on traditional classifiers, which lack consistency in methodology because they do not strictly adhere to the false-positive rate constraint. In this paper, we propose a novel scoring-thresholding approach, tau-False Positive Learning (tau-FPL) to address this problem. We show the scoring problem which takes the false-positive rate tolerance into accounts can be efficiently solved in linear time, also an out-of-bootstrap thresholding method can transform the learned ranking function into a low false-positive classifier. Both theoretical analysis and experimental results show superior performance of the proposed tau-FPL over existing approaches.