arXiv subjects

Qing Lu

Publications and source records attributed to Qing Lu.

At least 55 records · Page 3Linked to original sources

arXiv2021

Two-level overlapping Schwarz methods based on local generalized eigenproblems for Hermitian variational problems

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.

math.NA↗

arXiv2021

Superconductivity in ThMo2Si2C with Mo2C Square Net

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 Åand $c$ = 5.3571 Å. 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 $ΔC/γ_{\rm n}T$ = 0.98. The superconducting parameters of the critical magnetic fields, coherence length, penetration depth, and superconducting energy gap are given.

cond-mat.supr-con↗

arXiv2021

On the distribution of multivariate Jacobi sums

Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $q^{-(m-1)/2}J(χ_1,\dots,χ_m)$ ($χ_1\dotsm χ_m$ nontrivial) is asymptotically equidistributed on the unit circle, when $χ_1\in \mathcal{A}_1,\dots, χ_m\in \mathcal{A}_m$ run through arbitrary sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$, if $\#\mathcal{A}_1\ge q^{\frac{1}{2}+ε}$, $\#\mathcal{A}_2 \ge (\log q)^{\frac{1}δ-1}$ for $ε>δ>0$ 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.

math.NT↗

arXiv2021

A Kernel-Based Neural Network for High-dimensional Genetic Risk Prediction Analysis

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.

stat.ME↗

arXiv2020

The Layer-inserting Growth of Antiferromagnetic Topological Insulator MnBi$_2$Te$_4$ Based on Symmetry and Its X-ray Photoelectron Spectroscopy

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 $α$-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.

cond-mat.str-el↗

arXiv2020

Asymptotic Theory of Expectile Neural Networks

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.

math.ST↗

arXiv2020

Expectile Neural Networks for Genetic Data Analysis of Complex Diseases

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.

stat.AP↗

arXiv2020

Cost-effectiveness Analysis of Antiepidemic Policies and Global Situation Assessment of COVID-19

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.

physics.soc-ph↗

arXiv2020

NASS: Optimizing Secure Inference via Neural Architecture Search

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.

cs.CR↗

arXiv2019

On Neural Architecture Search for Resource-Constrained Hardware Platforms

In the recent past, the success of Neural Architecture Search (NAS) has enabled researchers to broadly explore the design space using learning-based methods. Apart from finding better neural network architectures, the idea of automation has also inspired to improve their implementations on hardware. While some practices of hardware machine-learning automation have achieved remarkable performance, the traditional design concept is still followed: a network architecture is first structured with excellent test accuracy, and then compressed and optimized to fit into a target platform. Such a design flow will easily lead to inferior local-optimal solutions. To address this problem, we propose a new framework to jointly explore the space of neural architecture, hardware implementation, and quantization. Our objective is to find a quantized architecture with the highest accuracy that is implementable on given hardware specifications. We employ FPGAs to implement and test our designs with limited loop-up tables (LUTs) and required throughput. Compared to the separate design/searching methods, our framework has demonstrated much better performance under strict specifications and generated designs of higher accuracy by 18\% to 68\% in the task of classifying CIFAR10 images. With 30,000 LUTs, a light-weight design is found to achieve 82.98\% accuracy and 1293 images/second throughput, compared to which, under the same constraints, the traditional method even fails to find a valid solution.

cs.LG↗

arXiv2019

Duality and nearby cycles over general bases

This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this commutation holds, confirming a prediction of Deligne. As an application we give a new proof of Beilinson's theorem that the vanishing cycle functor commutes with duality up to twist. Over an excellent base scheme, we show that the sliced nearby cycle functor commutes with duality up to modification of the base. We deduce that duality preserves universal local acyclicity over an excellent regular base. We also present Gabber's theorem that local acyclicity implies universal local acyclicity over a Noetherian base.

math.AG↗

arXiv2019

Asymptotic Properties of Neural Network Sieve Estimators

Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate any continuous function on a compact support as long as the number of hidden units is sufficiently large. Statistically, a neural network can be classified into a nonlinear regression framework. However, if we consider it parametrically, due to the unidentifiability of the parameters, it is difficult to derive its asymptotic properties. Instead, we considered the estimation problem in a nonparametric regression framework and use the results from sieve estimation to establish the consistency, the rates of convergence and the asymptotic normality of the neural network estimators. We also illustrate the validity of the theories via simulations.

math.ST↗

arXiv2019

Grand Challenge of 106-Point Facial Landmark Localization

Facial landmark localization is a very crucial step in numerous face related applications, such as face recognition, facial pose estimation, face image synthesis, etc. However, previous competitions on facial landmark localization (i.e., the 300-W, 300-VW and Menpo challenges) aim to predict 68-point landmarks, which are incompetent to depict the structure of facial components. In order to overcome this problem, we construct a challenging dataset, named JD-landmark. Each image is manually annotated with 106-point landmarks. This dataset covers large variations on pose and expression, which brings a lot of difficulties to predict accurate landmarks. We hold a 106-point facial landmark localization competition1 on this dataset in conjunction with IEEE International Conference on Multimedia and Expo (ICME) 2019. The purpose of this competition is to discover effective and robust facial landmark localization approaches.

cs.CV↗

arXiv2019

Compatible systems and ramification

We show that compatible systems of $\ell$-adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite field. As an application, we deduce the equicharacteristic case of classical conjectures on $\ell$-independence for proper smooth varieties over complete discrete valuation fields. Moreover, we show that compatible systems have compatible ramification. We also prove an analogue for integrality along the boundary.

math.AG↗

arXiv2018

Type-I and type-II Nodal Lines Coexistence in the Antiferromagnetic monolayer CrAs$_{2}$

Topological nodal line semimetals, hosting one-dimensional Fermi lines with symmetry protection, has become a hot topic in topological quantum matter. Due to the breaking of time reversal symmetry in magnetic system, nodal lines require protection by additional symmetries. Here, we report the discovery of antiferromagnetic type-I and type-II nodal lines coexist in the monolayer CrAs$_{2}$ based on a systematic first-principles calculation. Remarkably, the type-I nodal line in CrAs$_{2}$ form a concentric loop centered around the $Γ$ point is filling-enforced by nonsymmorphic analogue symmetry and robust against spin-orbital coupling. The type-II nodal lines, a kind of open nodal lines appear around the Fermi level, are protected by the mirror symmetry in the absence of spin-orbital coupling. The antiferromagnetic monolayer CrAs$_{2}$ proposed here may provide a platform for the correlation between magnetism and exotic topological phases.

cond-mat.mtrl-sci↗

arXiv2018

Quantization of Fully Convolutional Networks for Accurate Biomedical Image Segmentation

With pervasive applications of medical imaging in health-care, biomedical image segmentation plays a central role in quantitative analysis, clinical diagno- sis, and medical intervention. Since manual anno- tation su ers limited reproducibility, arduous e orts, and excessive time, automatic segmentation is desired to process increasingly larger scale histopathological data. Recently, deep neural networks (DNNs), par- ticularly fully convolutional networks (FCNs), have been widely applied to biomedical image segmenta- tion, attaining much improved performance. At the same time, quantization of DNNs has become an ac- tive research topic, which aims to represent weights with less memory (precision) to considerably reduce memory and computation requirements of DNNs while maintaining acceptable accuracy. In this paper, we apply quantization techniques to FCNs for accurate biomedical image segmentation. Unlike existing litera- ture on quantization which primarily targets memory and computation complexity reduction, we apply quan- tization as a method to reduce over tting in FCNs for better accuracy. Speci cally, we focus on a state-of- the-art segmentation framework, suggestive annotation [22], which judiciously extracts representative annota- tion samples from the original training dataset, obtain- ing an e ective small-sized balanced training dataset. We develop two new quantization processes for this framework: (1) suggestive annotation with quantiza- tion for highly representative training samples, and (2) network training with quantization for high accuracy. Extensive experiments on the MICCAI Gland dataset show that both quantization processes can improve the segmentation performance, and our proposed method exceeds the current state-of-the-art performance by up to 1%. In addition, our method has a reduction of up to 6.4x on memory usage.

cs.CV↗

arXiv2018

Robust Large Gap Quantum Spin Hall Insulators in Methyl-functionalized III-Bi Buckled Honeycombs

A large bulk band gap is critical for the applications of quantum spin hall (QSH) insulators in spintronics at room temperature. Based on first-principles calculations, we predict that the methyl-functionalized III-Bi monolayers, namely III-Bi-(CH3)2 (III=Ga, In, Tl) thin films, own QSH states with band gap as large as 0.260, 0.304 and 0.843 eV, respectively, making them suitable for room-temperature applications. The topological characteristics are confirmed by s-px,y band inversion, topological invariant Z2, and the topologically protected edge states. Noticeably, for GaBi/InBi-(CH3)2 films, the s-px,y band inversion occurred in the progress of spin-orbital coupling (SOC), while for TlBi(CH3)2 film, the s-px,y band inversion happened in the progress of chemical bonding. Significantly, the QSH states in III-Bi-(CH3)2 films are robust against the mechanical strains and various methyl coverages, making these films particularly flexible to substrate choice for device applications. Besides, the h-BN substrate is an ideal substrate for III-Bi-(CH3)2 films to realize large gap nontrivial topological states.. These findings demonstrate that the methyl-functionalized III-Bi films may be good QSH effect platforms for topological electronic devices design and fabrication in spintronics.

cond-mat.mtrl-sci↗

arXiv2018

Generalized Similarity U: A Non-parametric Test of Association Based on Similarity

Second generation sequencing technologies are being increasingly used for genetic association studies, where the main research interest is to identify sets of genetic variants that contribute to various phenotype. The phenotype can be univariate disease status, multivariate responses and even high-dimensional outcomes. Considering the genotype and phenotype as two complex objects, this also poses a general statistical problem of testing association between complex objects. We here proposed a similarity-based test, generalized similarity U (GSU), that can test the association between complex objects. We first studied the theoretical properties of the test in a general setting and then focused on the application of the test to sequencing association studies. Based on theoretical analysis, we proposed to use Laplacian kernel based similarity for GSU to boost power and enhance robustness. Through simulation, we found that GSU did have advantages over existing methods in terms of power and robustness. We further performed a whole genome sequencing (WGS) scan for Alzherimer Disease Neuroimaging Initiative (ADNI) data, identifying three genes, APOE, APOC1 and TOMM40, associated with imaging phenotype. We developed a C++ package for analysis of whole genome sequencing data using GSU. The source codes can be downloaded at https://github.com/changshuaiwei/gsu.

stat.ME↗