This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrix can reduce the computational effort of the DQM for calculations of the inverse, determinant, eigenvectors and eigenvalues by 75%. This computational advantage are also demonstrated via several numerical examples.

W Chen Xinwei Wang Yongxi Yu

We consider the Euler-Poincar\'e equation on $\mathbb R^d$, $d\ge 2$. For a large class of smooth initial data we prove that the corresponding solution blows up in finite time. This settles an open problem raised by Chae and Liu \cite{Chae Liu}. Our analysis exhibits some new concentration mechanism and hidden monotonicity formula associated with the Euler-Poincar\'e flow. In particular we show the abundance of blowups emanating from smooth initial data with certain sign properties. No size restrictions are imposed on the data. We also showcase a class of initial data for which the corresponding solution exists globally in time.

Dong Li Xinwei Yu Zhichun Zhai

Fithian and Hastie (2014) proposed a new sampling scheme called local case-control (LCC) sampling that achieves stability and efficiency by utilizing a clever adjustment pertained to the logistic model. It is particularly useful for classification with large and imbalanced data. This paper proposes a more general sampling scheme based on a working principle that data points deserve higher sampling probability if they contain more information or appear "surprising" in the sense of, for example, a large error of pilot prediction or a large absolute score. Compared with the relevant existing sampling schemes, as reported in Fithian and Hastie (2014) and Ai, et al. (2018), the proposed one has several advantages. It adaptively gives out the optimal forms to a variety of objectives, including the LCC and Ai et al. (2018)'s sampling as special cases. Under same model specifications, the proposed estimator also performs no worse than those in the literature. The estimation procedure is valid even if the model is misspecified and/or the pilot estimator is inconsistent or dependent on full data. We present theoretical justifications of the claimed advantages and optimality of the estimation and the sampling design. Different from Ai, et al. (2018), our large sample theory are population-wise rather than data-wise. Moreover, the proposed approach can be applied to unsupervised learning studies, since it essentially only requires a specific loss function and no response-covariate structure of data is needed. Numerical studies are carried out and the evidence in support of the theory is shown.

Xinwei Shen Kani Chen Wen Yu

In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed estimator is robust to the presence of finite variation jumps in price processes. The related functional central limit theorem for the proposed estimator has been established. Compared with the estimator with non-overlapped increments, the estimator with overlapped increments improves the asymptotic estimation efficiency. Moreover, we study the asymptotic theory of estimator under a long-span setting and employ it to create a feasible test for the dependence between volatilities. Finally, simulation and empirical studies demonstrate the performance of proposed estimators.

XinWei Feng Yu Jiang Zhi Liu Zhe Meng

Recent work has demonstrated the vulnerability of modern text classifiers to universal adversarial attacks, which are input-agnostic sequences of words added to text processed by classifiers. Despite being successful, the word sequences produced in such attacks are often ungrammatical and can be easily distinguished from natural text. We develop adversarial attacks that appear closer to natural English phrases and yet confuse classification systems when added to benign inputs. We leverage an adversarially regularized autoencoder (ARAE) to generate triggers and propose a gradient-based search that aims to maximize the downstream classifier's prediction loss. Our attacks effectively reduce model accuracy on classification tasks while being less identifiable than prior models as per automatic detection metrics and human-subject studies. Our aim is to demonstrate that adversarial attacks can be made harder to detect than previously thought and to enable the development of appropriate defenses.

Liwei Song Xinwei Yu Hsuan-Tung Peng Karthik Narasimhan

In this paper, we generalize the main results of [1] and [31] to Lorentz spaces, using a simple procedure. The main results are the following. Let $n\geq 3$ and let $u$ be a Leray-Hopf solution to the $n$-dimensional Navier-Stokes equations with viscosity $\nu$ and divergence free initial condition $u_0\in L^2(\mathbb{R}^n)\cap L^{k}(\mathbb{R}^n)$ (where $k=k(s)$ is sufficiently large). Then there exists a constant $c>0$ such that if \begin{equation} \|p\|_{L^{r,\infty}(0,\infty;L^{s,\infty}(\mathbb{R}^n))}<c\hspace{10mm}\frac{n}{s}+\frac{2}{r}\leq 2,\hspace{5mm}s>\frac{n}{2} \end{equation} or \begin{equation} \|\nabla p\|_{L^{r,\infty}(0,\infty;L^{s,\infty}(\mathbb{R}^n))}<c\hspace{10mm}\frac{n}{s}+\frac{2}{r}\leq 3,\hspace{5mm}s>\frac{n}{3} \end{equation} then $u$ is smooth on $(0, \infty) \times \mathbb{R}^n$. Partial results in the case $n=3$ were obtained in [32], [33] and then recently extended to all appropriate pairs of $r,s$ in [14]. Our results present a unified proof which works for all dimensions $n\geq 3$ and the full range or admissible pairs, $(s,r)$.

Benjamin Pineau Xinwei Yu

This letter proposes a modified non-orthogonal multiple-access (NOMA) scheme for systems with a multi-antenna base station (BS) and two single-antenna users, where NOMA transmissions are conducted only when the absolute correlation coefficient (CC) between the user channels exceeds a threshold and the BS uses matched-filter (MF) precoding along the user with the stronger average channel gain. We derive the average minimal transmit power to guarantee the signal-to-interference-plus-noise-ratio (SINR) levels of both users. Our results show that the average minimal power grows logarithmically in the reciprocal of the CC threshold and a non-zero threshold is necessary for the modified NOMA scheme to have finite average minimal transmit power. Further, for the massive MIMO scenario, we derive the scaling laws of the average transmit power and outage probability with respect to the antenna numbers, as well as their tradeoff law. Simulation results are shown to validate our theoretical results.

Zeyu Sun Yindi Jing Xinwei Yu

We perform core-level X-ray photoemission spectroscopy (XPS) and electronic Raman scattering studies of electronic structures and spin fluctuations in the bulk samples of the nickelate oxide NdNiO$_2$. According to Nd $3d$ and O $1s$ XPS spectra, we conclude that NdNiO$_2$ has a large transfer energy. From the analysis of the main line of the Ni $2p_{3/2}$ XPS, we confirm the NiO$_2$ planes in NdNiO$_2$ are of Mott-Hubbard type in the Zaanen-Sawatzky-Allen scheme. The two-magnon peak in the Raman scattering provides direct evidence for the strong spin-fluctuation in NdNiO$_2$. The peak position determines the antiferromagnetic exchange $J=25$~meV. Our experimental results agree well with our previous theoretical results.

Ying Fu Le Wang Hu Cheng Shenghai Pei Xuefeng Zhou Jian Chen Shaoheng Wang Ran Zhao Wenrui Jiang Cai Liu Mingyuan Huang XinWei Wang Yusheng Zhao Dapeng Yu Fei Ye Shanmin Wang Jia-Wei Mei

The utilization of renewable energy technologies, particularly hydrogen, has seen a boom in interest and has spread throughout the world. Ethanol steam reformation is one of the primary methods capable of producing hydrogen efficiently and reliably. This paper provides an in-depth study of the reformulated system both theoretically and numerically, as well as a plan to explore the possibility of converting the system into its conservation form. Lastly, we offer an overview of several numerical approaches for solving the general first-order quasi-linear hyperbolic equation to the particular model for ethanol steam reforming (ESR). We conclude by presenting some results that would enable the usage of these ODE/PDE solvers to be used in non-linear model predictive control (NMPC) algorithms and discuss the limitations of our approach and directions for future work.

Robert Joseph George Xinwei Yu

Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in constraint-based causal discovery for identifying causal relations. To address this issue, existing methods introduced proxy variables to adjust for the bias caused by unobserveness. However, these methods were either limited to categorical variables or relied on strong parametric assumptions for identification. In this paper, we propose a novel hypothesis-testing procedure that can effectively examine the existence of the causal relationship over continuous variables, without any parametric constraint. Our procedure is based on discretization, which under completeness conditions, is able to asymptotically establish a linear equation whose coefficient vector is identifiable under the causal null hypothesis. Based on this, we introduce our test statistic and demonstrate its asymptotic level and power. We validate the effectiveness of our procedure using both synthetic and real-world data.

Mingzhou Liu Xinwei Sun Yu Qiao Yizhou Wang