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The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and too heavy computational cost of coarse space construction. In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the algorithmic and theoretical frameworks of the corresponding TL-OS methods. Furthermore, to enhance the practicability of the algorithm, we design two economical TL-OS preconditioners and prove the condition number estimate. As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of second order elliptic problem with high contrast and oscillatory coefficient and the condition number of the TL-OS preconditioned system is robust with respect to the model and mesh parameters. In particular, we also prove that the condition number of the economically preconditioned system is independent of the jump range under a certain jump distribution. Experimental results show that the first kind of economical preconditioner is more efficient and stable than the existed one. Secondly, we construct TL-OS and the economical TL-OS preconditioners for the plane wave least squares discrete system of Helmholtz equation by using the frameworks. The numerical results for homogeneous and non-homogeneous cases illustrate that the PCG method based on the proposed preconditioners have good stability in terms of the angular frequency, mesh parameters and the number of degrees of freedom in each element.

Deep neural networks (DNNs) have demonstrated their great potential in recent years, exceeding the per-formance of human experts in a wide range of applications. Due to their large sizes, however, compressiontechniques such as weight quantization and pruning are usually applied before they can be accommodated onthe edge. It is generally believed that quantization leads to performance degradation, and plenty of existingworks have explored quantization strategies aiming at minimum accuracy loss. In this paper, we argue thatquantization, which essentially imposes regularization on weight representations, can sometimes help toimprove accuracy. We conduct comprehensive experiments on three widely used applications: fully con-nected network (FCN) for biomedical image segmentation, convolutional neural network (CNN) for imageclassification on ImageNet, and recurrent neural network (RNN) for automatic speech recognition, and experi-mental results show that quantization can improve the accuracy by 1%, 1.95%, 4.23% on the three applicationsrespectively with 3.5x-6.4x memory reduction., Comment: 11 pages, 3 figures, 10 tables, accepted by the ACM Journal on Emerging Technologies in Computing Systems (JETC)

We report the superconductivity of a new quaternary compound ThMo$_2$Si$_2$C, synthesized with the arc-melting technique. The compound crystallizes in a tetragonal CeCr$_2$Si$_2$C-type structure with cell parameters of $a$ = 4.2296 \r{A}and $c$ = 5.3571 \r{A}. An interlayer Si-Si covalent bonding is suggested by the atomic distance. The electrical resistivity and magnetic susceptibility measurements indicate a Pauli-paramagnetic metal with dominant electron-electron scattering in the normal-state. Bulk superconductivity at 2.2 K is demonstrated with a dimensionless specific-heat jump of ${\Delta}C/\gamma_{\rm n}T$ = 0.98. The superconducting parameters of the critical magnetic fields, coherence length, penetration depth, and superconducting energy gap are given., Comment: 14 pages, 6 figures, 3 tables. Accepted for publication in SCIENCE CHINA Physics, Mechanics & Astronomy

There is long research interest in electron-induced reactions of halogenated molecules. It has been two decades since the cosmic-ray (CR) driven electron-induced reaction (CRE) mechanism for the ozone hole formation was proposed. The derived CRE equation with stratospheric equivalent chlorine level and CR intensity as only two variables has well reproduced the observed data of stratospheric O3 and temperatures over the past 40 years. The CRE predictions of 11-year cyclic variations of the Antarctic O3 hole and associated stratospheric cooling have also been well confirmed. Measured altitude profiles of ozone and temperatures in Antarctic ozone holes provide convincing fingerprints of the CRE mechanism. A quantitative estimate indicates that the CRE-produced Cl atoms could completely deplete or even over-kill ozone in the CR-peak polar stratospheric region, consistent with observed altitude profiles of severest Antarctic ozone holes. After removing the natural CR effect, the hidden recovery in the Antarctic O3 hole since around 1995 is clearly discovered, while the recovery of O3 loss at mid-latitudes is being delayed by >=10 years. These results have provided strong evidence of the CRE mechanism. If the CR intensity keeps the current rising trend, the Antarctic O3 hole will return to the 1980 level by around 2060, while the returning of the O3 layer at mid-latitudes to the 1980 level will largely be delayed or will not even occur by the end of this century. The results strongly indicate that the CRE mechanism must be considered as a key factor in evaluating the O3 hole., Comment: 23 pages, 8 figures

Risk prediction capitalizing on emerging human genome findings holds great promise for new prediction and prevention strategies. While the large amounts of genetic data generated from high-throughput technologies offer us a unique opportunity to study a deep catalog of genetic variants for risk prediction, the high-dimensionality of genetic data and complex relationships between genetic variants and disease outcomes bring tremendous challenges to risk prediction analysis. To address these rising challenges, we propose a kernel-based neural network (KNN) method. KNN inherits features from both linear mixed models (LMM) and classical neural networks and is designed for high-dimensional risk prediction analysis. To deal with datasets with millions of variants, KNN summarizes genetic data into kernel matrices and use the kernel matrices as inputs. Based on the kernel matrices, KNN builds a single-layer feedforward neural network, which makes it feasible to consider complex relationships between genetic variants and disease outcomes. The parameter estimation in KNN is based on MINQUE and we show, that under certain conditions, the average prediction error of KNN can be smaller than that of LMM. Simulation studies also confirm the results.

Correlated outcomes are common in many practical problems. In some settings, one outcome is of particular interest, and others are auxiliary. To leverage information shared by all the outcomes, traditional multi-task learning (MTL) minimizes an averaged loss function over all the outcomes, which may lead to biased estimation for the target outcome, especially when the MTL model is mis-specified. In this work, based on a decomposition of estimation bias into two types, within-subspace and against-subspace, we develop a robust transfer learning approach to estimating a high-dimensional linear decision rule for the outcome of interest with the presence of auxiliary outcomes. The proposed method includes an MTL step using all outcomes to gain efficiency, and a subsequent calibration step using only the outcome of interest to correct both types of biases. We show that the final estimator can achieve a lower estimation error than the one using only the single outcome of interest. Simulations and real data analysis are conducted to justify the superiority of the proposed method., Comment: 19 pages, 2 figures

Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When the size of parameter is too large, the standard maximum likelihood procedures may not work. We use sieve method to constrain parameter space. And we prove its consistency and normality under nonparametric regression framework.

The genetic etiologies of common diseases are highly complex and heterogeneous. Classic statistical methods, such as linear regression, have successfully identified numerous genetic variants associated with complex diseases. Nonetheless, for most complex diseases, the identified variants only account for a small proportion of heritability. Challenges remain to discover additional variants contributing to complex diseases. Expectile regression is a generalization of linear regression and provides completed information on the conditional distribution of a phenotype of interest. While expectile regression has many nice properties and holds great promise for genetic data analyses (e.g., investigating genetic variants predisposing to a high-risk population), it has been rarely used in genetic research. In this paper, we develop an expectile neural network (ENN) method for genetic data analyses of complex diseases. Similar to expectile regression, ENN provides a comprehensive view of relationships between genetic variants and disease phenotypes and can be used to discover genetic variants predisposing to sub-populations (e.g., high-risk groups). We further integrate the idea of neural networks into ENN, making it capable of capturing non-linear and non-additive genetic effects (e.g., gene-gene interactions). Through simulations, we showed that the proposed method outperformed an existing expectile regression when there exist complex relationships between genetic variants and disease phenotypes. We also applied the proposed method to the genetic data from the Study of Addiction: Genetics and Environment(SAGE), investigating the relationships of candidate genes with smoking quantity.

Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $q^{-(m-1)/2}J(\chi_1,\dots,\chi_m)$ ($\chi_1\dotsm \chi_m$ nontrivial) is asymptotically equidistributed on the unit circle, when $\chi_1\in \mathcal{A}_1,\dots, \chi_m\in \mathcal{A}_m$ run through arbitrary sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$, if $\#\mathcal{A}_1\ge q^{\frac{1}{2}+\epsilon}$, $\#\mathcal{A}_2 \ge (\log q)^{\frac{1}{\delta}-1}$ for $\epsilon>\delta>0$ fixed and $q\to \infty$ or if $\#\mathcal{A}_1\#\mathcal{A}_2/q\to \infty$. This extends previous results of Xi, Z. Zheng, and the authors., Comment: 6 pages. v3: added more details

We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualizability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalizing a theorem of Gabber., Comment: 27 pages. v4: minor improvements. To appear in Forum of Mathematics, Sigma

With a two-layer contact-dispersion model and data in China, we analyze the cost-effectiveness of three types of antiepidemic measures for COVID-19: regular epidemiological control, local social interaction control, and inter-city travel restriction. We find that: 1) intercity travel restriction has minimal or even negative effect compared to the other two at the national level; 2) the time of reaching turning point is independent of the current number of cases, and only related to the enforcement stringency of epidemiological control and social interaction control measures; 3) strong enforcement at the early stage is the only opportunity to maximize both antiepidemic effectiveness and cost-effectiveness; 4) mediocre stringency of social interaction measures is the worst choice. Subsequently, we cluster countries/regions into four groups based on their control measures and provide situation assessment and policy suggestions for each group.

There is no vaccine or specific antiviral treatment for COVID-19. One current focus is drug repurposing research, but those drugs have limited therapeutic efficacies and known adverse effects. The pathology of COVID-19 is essentially unknown. It is therefore challenging to discover a successful treatment to be approved for clinical use. This paper addresses several key biological processes of reactive oxygen, halogen and nitrogen species (ROS, RHS and RNS) that play crucial physiological roles in organisms from plants to humans. These include why superoxide dismutases, the enzymes to catalyze the formation of H2O2, are required for protecting ROS-induced injury in cell metabolism, why the amount of ROS/RNS produced by ionizing radiation at clinically relevant doses is ~1000 fold lower than the endogenous ROS/RNS level routinely produced in the cell and why a low level of endogenous RHS plays a crucial role in phagocytosis for immune defense. Herein we propose a plausible amplification mechanism in immune defense: ozone-depleting-like halogen cyclic reactions enhancing RHS effects are responsible for all the mentioned physiological functions, which are activated by H2O2 and deactivated by NO signaling molecule. Our results show that the reaction cycles can be repeated thousands of times and amplify the RHS pathogen-killing (defense) effects by 100,000 fold in phagocytosis, resembling the cyclic ozone-depleting reactions in the stratosphere. It is unraveled that H2O2 is a required protective signaling molecule (angel) in the defense system for human health and its dysfunction can cause many diseases or conditions such as autoimmune disorders, aging and cancer. We also identify a class of potent drugs for effective treatment of invading pathogens such as HIV and SARS-CoV-2 (COVID-19), cancer and other diseases, and provide a molecular mechanism of action of the drugs or candidates., Comment: 18 pages, 4 figures, 1 table

The antiferromagnetic topological insulator has attracted lots of attention recently, as its intrinsic magnetism and topological property makes it a potential material to realize the quantum anomalous Hall effect (QAHE) at relative high temperature. Until now, only MnBi$_2$Te$_4$ is predicted and grown successfully. The other MB$_2$T$_4$-family materials predicted (MB$_2$T$_4$:M=transition-metal or rare-earth element, B=Bi or Sb, T=Te, Se, or S) with not only antiferromagnetic topological property but also rich and exotic topological quantum states and dynamically stable (or metastable) structure have not been realized on experiment completely. Here, MnBi$_2$Te$_4$ single crystals have been grown successfully and tested. It shows typical antiferromagnetic character, with Neel temperature of 24.5K and a spin-flop transition at H$\thickapprox$35000 Oe, 1.8K. After obtaining MnBi$_2$Te$_4$ single crystals, we have tried to synthesize the other members of MB$_2$T$_4$-family materials, but things are not going so well. Then it inspires us to discuss the growth mechanism of MnBi$_2$Te$_4$. The growth mode may be the layer-inserting growth mode based on symmetry, which is supported by our X-ray photoelectron spectroscopy (XPS) measurement. The XPS measurement combing with the $Ar^+$ ion sputtering is done to investigate the chemical state of MnBi$_2$Te$_4$. Binding energies (BE) of the MnBi$_2$Te$_4$-related contributions to Mn2p and Te3d spectra agree well with those of inserting material $\alpha$-MnTe. Rising intensity of the Mn2p satellite for divalent Mn (bound to chalcogen) with atomic number of ligand (from MnO to MnBi$_2$Te$_4$) has been observed, thus suggesting classification of MnBi$_2$Te$_4$ as the charge-transfer compound. Understanding the growth mode of MnBi$_2$Te$_4$ can help us to grow the other members of MB$_2$T$_4$-family materials.

Due to increasing privacy concerns, neural network (NN) based secure inference (SI) schemes that simultaneously hide the client inputs and server models attract major research interests. While existing works focused on developing secure protocols for NN-based SI, in this work, we take a different approach. We propose NASS, an integrated framework to search for tailored NN architectures designed specifically for SI. In particular, we propose to model cryptographic protocols as design elements with associated reward functions. The characterized models are then adopted in a joint optimization with predicted hyperparameters in identifying the best NN architectures that balance prediction accuracy and execution efficiency. In the experiment, it is demonstrated that we can achieve the best of both worlds by using NASS, where the prediction accuracy can be improved from 81.6% to 84.6%, while the inference runtime is reduced by 2x and communication bandwidth by 1.9x on the CIFAR-10 dataset., Comment: 8 pages, 6 figures, in Proceedings of ECAI 2020, the 24th European Conference on Artificial Intelligence