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On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

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Science China Mathematics 2023年第11期66卷 2615-2640页

作者： Zeng Li Cheng Wang Qinwen Wang Department of Statistics and Data Science Southern University of Science and TechnologyShenzhen 518055China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Shanghai Jiao Tong University) Shanghai 200240China School of Data Science Fudan UniversityShanghai 200433China

In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation *** underlying population is allowed to have a general dependence *** result no longer follows the generalized Marcenko-Pastur law,which is brand *** is the first result on rank correlation matrices with *** applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance *** these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.

关键词： Hoeffding decomposition Kendall's rank correlation matrix limiting spectral distribution random matrix theory

A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM

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arXiv 2021年

作者： Tian, Wei Jingjing, Huang Chen, Rongliang Jiang, Yi Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen518055 China Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen518055 China Department of Rehabilitation Medicine Shenzhen University General Hospital Shenzhen518055 China

In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the computational mesh into two types of subdomains: the regular subdomains and the crack tip subdomains based on the observation that the crack tips have a significant impact on the convergence of the iterative method while the impact of the crack lines is not that different from those of regular mesh points. The tip subdomains consist of mesh points at crack tips and all neighboring points where the branch enrichment functions are applied. The regular subdomains consist of all other mesh points, including those on the crack lines. To overcome the mismatch between the number of subdomains and the number of processor cores, the proposed method is divided into two steps: solve the crack tip problem and then the regular subdomain problem during each iteration. The proposed method was used to develop a parallel XFEM package which is able to test different types of iterative methods. To achieve good parallel efficiency, additional methods were introduced to reduce communication and to maintain the load balance between processors. Numerical experiments indicate that the proposed method significantly reduces the number of iterations and the total computation time compared to the classical methods. In addition, the method scales up to 8192 processor cores with over 70% parallel efficiency to solve problems with more than 2 × 108 degrees of freedom. Copyright © 2021, The Authors. All rights reserved.

关键词： Crack tips

Efficient parallel simulation of blood flows in abdominal aorta

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arXiv 2019年

作者： Qin, Shanlin Chen, Rongliang Wu, Bokai Liu, Jia Shiu, Wen-Shin Yan, Zhengzheng Cai, Xiao-Chuan Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences China Department of Computer Science University of Colorado BoulderCO80309-0430 United States

It is known that the maximum diameter for the rupture-risk assessment of the abdominal aortic aneurysm is a generally good method, but not sufficient. Alternative features obtained with computational modeling may provide additional useful criteria. Though computational approaches are noninvasive, they are often time-consuming because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta. We model the blood flow with the unsteady incompressible Navier-Stokes equations, and solve the discretized system with a highly scalable domain decomposition method. With this approach, the complete flow field can be obtained in less than an hour, instead of days with older methods. We show experimentally that the proposed method offers accurate solutions of the pressure, the velocity and the wall shear stress, and the parallel efficiency is higher than 70% on a parallel computer with more than 1, 000 processor cores. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Pose Estimation for Non-Cooperative Spacecraft Based on Deep Learning

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SSRN

SSRN 2024年

作者： Gao, Xiang Liu, Chang Liu, Jia Hu, Weiduo Shenzhen Aerospace Dongfanghong Satellite Ltd Guangdong Shenzhen518052 China Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Guangdong Shenzhen518052 China Beihang University Beijing100191 China Total Design Department Institute of Advanced Computing and Digital Engineering Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing China School of Astronautics

This paper proposes an end-to-end pose estimation framework for spacecraft. The framework can run on full-size images and jointly calculate translation and rotation parameters based on shared features of convolutional network. In addition, we introduce the method of label normalization. In the training stage, images and labels are normalized and then input into the neural network architecture for training. In the test stage, the normalized images are input to the trained framework, and the corresponding predicted pose is obtained after the output parameters are reversely normalized. Then we use the local optimization method to optimize the predicted pose. The effectiveness of our method is verified by a large number of experiments. © 2024, The Authors. All rights reserved.

关键词： Network architecture

Non-invasive assessment of intracranial wall shear stress using high-resolution magnetic resonance imaging in combination with computational fluid dynamics technique

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Fundamental Research 2022年第2期2卷 329-334页

作者： Yuwen Chen Jia Liu Mingli Li Yannan Yu Zhengzheng Yan Wenshin Shiu Bokai Wu Zaiheng Cheng Yao Meng Yang Liu Weizhuang Yuan Zongmuyu Zhang Weihai Xu Department of Neurology State Key Laboratory of Complex Severe and Rare DiseasesPeking Union Medical Cllege HospitalChinese Academy of Medical Sciences and Peking Union Medical College1 ShuaifuyuanBeijing 100005China Department of Cardiology Second Afliated Hospital of Zhejiang University School of MedicineHangzhouZhejiang 310009China Shenzhen Instiutes of Advanced Technology Chinese Academy of SciencesShenzhen 518055China Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen 518055China Department of Radiology Peking Union Medical College HospitalChinese Acadermy of Medical Sciences1 ShuaifiryuanBeijing 100005China Department of Radiology Stanford UniversityCaliformia 94305United States Department of Neurology Saarland UniversityKirrberger StraSe 66421Germany

In vivo studies on association between wall shear stress(WSS)and intracranial plaque are *** on the three-dimensional T1-weighted high-resolution magnetic resonance imaging(3DT1 HR-MRI)data of patients with low-grade stenotic(<50%)atherosclerotic middle cerebral artery(MCA)and subjects with normal MCA,we built a three-dimensional reconstructed WSS model by computational fluid dynamics(CFD)***-dimensional registration of the CFD model to the HR-MRI was performed with projections based on the resolution and thickness of the *** relationships between the Wss at each side of the vessel wall and plaque location were analyzed.A total of 94 MCA plaques from 43 patients and 50 normal MCAs were *** the normal MCAs,WSS was lower at the ventral-inferior wall than at the dorsal-superior wall(proximal segment,p<0.001;middle segment,p<0.001)and lower at the inner wall than at the outer wall of the MCA curve(p<0.001).In atherosclerotic MCAs,similar low Wss regions were observed where plaques *** WSS ratio of the ventral-inferior wall to the dorsal-superior wall in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).The WSS_(inmer-outer)ratio in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).Low WSS was associated with MCA atherosclerosis formation and occurred mainly at the ventral inferior wall,which was anatomically opposite the orifices of penetrating arteries,and at the inner wall of the MCA ***,the results were well consistent with the low WSS theory in atherosclerosis *** reconstructed WSS model is a promising novel method for assessing an individualized vascular profile once validated by further studies.

关键词： Intracranial atherosclerosis Wall shear stress Atherosclerotic plaque High-resolution magnetic resonance imaging Computational fluid dynamics

Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

HPE Transformer: Learning to Optimize Multi-Group Multicast Beamforming Under Nonconvex QoS Constraints

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arXiv 2024年

作者： Li, Yang Liu, Ya-Feng The Shenzhen Research Institute of Big Data Shenzhen518172 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper studies the quality-of-service (QoS) constrained multi-group multicast beamforming design problem, where each multicast group is composed of a number of users requiring the same content. Due to the nonconvex QoS constraints, this problem is nonconvex and NP-hard. While existing optimization-based iterative algorithms can obtain a suboptimal solution, their iterative nature results in large computational complexity and delay. To facilitate real-time implementations, this paper proposes a deep learning-based approach, which consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users, different numbers of multicast groups, and different signal-to-interference-plus-noise ratio targets. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

Investigating different syntactic context types and context representations for learning word embeddings

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Investigating different syntactic context types and context ...

2017 Conference on Empirical Methods in Natural Language Processing, EMNLP 2017

作者： Li, Bofang Liu, Tao Zhao, Zhe Tang, Buzhou Drozd, Aleksandr Rogers, Anna Du, Xiaoyong School of Information Renmin University of China China Key Laboratory of Data Engineering and Knowledge Engineering MOE China Shenzhen Graduate School Harbin Institute of Technology China Global Scientific Information and Computing Center Tokyo Institute of Technology China Department of Computer Science University of Massachusetts Lowell United States

ISBN: (纸本)9781945626838

The number of word embedding models is growing every year. Most of them are based on the co-occurrence information of words and their contexts. However, it is still an open question what is the best definition of context. We provide a systematical investigation of 4 different syntactic context types and context representations for learning word embeddings. Comprehensive experiments are conducted to evaluate their effectiveness on 6 extrinsic and intrinsic tasks. We hope that this paper, along with the published code, would be helpful for choosing the best context type and representation for a given task. © 2017 Association for Computational Linguistics.

关键词： Embeddings

Efficient Estimation of Sensor Biases for the 3-Dimensional Asynchronous Multi-Sensor System

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arXiv 2021年

作者： Pu, Wenqiang Liu, Ya-Feng Luo, Zhi-Quan Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

An important preliminary procedure in multi-sensor data fusion is sensor registration, and the key step in this procedure is to estimate sensor biases from their noisy measurements. There are generally two difficulties in this bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, and the other is the highly nonlinear coordinate transformation between the local and global coordinate systems of the sensors. In this paper, we focus on the 3-dimensional asynchronous multi-sensor scenario and propose a weighted nonlinear least squares (NLS) formulation by assuming that there is a target moving with a nearly constant velocity. We propose two possible choices of the weighting matrix in the NLS formulation, which correspond to classical and weighted NLS estimation and maximum likelihood (ML) estimation, respectively. To address the intrinsic nonlinearity, we propose a block coordinate descent (BCD) algorithm for solving the formulated problem, which alternately updates different kinds of bias estimates. Specifically, the proposed BCD algorithm involves solving linear LS problems and nonconvex quadratically constrained quadratic program (QCQP) problems with special structures. Instead of adopting the semidefinite relaxation technique, we develop a much more computationally efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve the nonconvex QCQP subproblems. The convergence of the ADMM to the global solution of the QCQP subproblems is established under mild conditions. The effectiveness and efficiency of the proposed BCD algorithm are demonstrated via numerical simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： Maximum likelihood estimation