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GRAPH SPARSIFICATION BY UNIVERSAL GREEDY ALGORITHMS

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Journal of Computational Mathematics 2023年第4期41卷 741-770页

作者： ming-jun lai Jiaxin Xie Zhiqiang Xu Department of Mathematics University of GeorgiaAthensGA 30602USA LMIB of the Ministry of Education School of Mathematical SciencesBeihang UniversityBeijing 100191China LSEC Inst.Comp.Math.Academy of Mathematics and System ScienceChinese Academy of SciencesBeijing 100091China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications,such as simplification of social networks,least squares problems,and numerical solution of symmetric positive definite linear *** this paper,inspired by the well-known sparse signal recovery algorithm called orthogonal matching pursuit(OMP),we introduce a deterministic,greedy edge selection algorithm,which is called the universal greedy approach(UGA)for the graph sparsification *** a general spectral sparsification problem,e.g.,the positive subset selection problem from a set of m vectors in R n,we propose a nonnegative UGA algorithm which needs O(mn^(2)+n^(3)/ϵ^(2))time to find a 1+ϵ/β/1-ϵ/β-spectral sparsifier with positive coefficients with sparsity at most[n/ϵ^(2)],where β is the ratio between the smallest length and largest length of the *** convergence of the nonnegative UGA algorithm is *** the graph sparsification problem,another UGA algorithm is proposed which can output a 1+O(ϵ)/1-O(ϵ)-spectral sparsifier with[n/ϵ^(2)]edges in O(m+n^(2)/ϵ^(2))time from a graph with m edges and n vertices under some mild *** is a linear time algorithm in terms of the number of edges that the community of graph sparsification is looking *** best result in the literature to the knowledge of the authors is the existence of a deterministic algorithm which is almost linear,i.e.O(m^(1+o(1)))for some o(1)=O((log log(m))^(2/3)/log^(1/3)(m)).Finally,extensive experimental results,including applications to graph clustering and least squares regression,show the effectiveness of proposed approaches.

关键词： Spectral sparsification Subset selection Greedy algorithms Graph clustering Linear sketching

RECONSTRUCTION OF SPARSE POLYNOMIALS VIA QUASI-ORTHOGONAL MATCHING PURSUIT METHOD

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Journal of Computational Mathematics 2023年第1期41卷 18-38页

作者： Renzhong Feng Aitong Huang ming-jun lai Zhaiming Shen School of Mathematics Science&Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationBeihang UniversityBeijing 100191China Department of Mathematics University of GeorgiaAthensGA 30602U.S.A

In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal *** the two kinds of sampled data,data with noises and without noises,we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials,Chebyshev polynomials and trigonometric polynomials in s step *** results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal ***,numerical experiments will be presented to verify the effectiveness of the QOMP method.

关键词： Reconstruction of sparse polynomial Compressive sensing Mutual coherence Quasi-orthogonal matching pursuit algorithm

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数值差商公式研究

中国科学（A辑） 2005年第6期35卷 712-720页

作者：王兴华王何宇 ming-jun lai 浙江大学数学系杭州310028

分别针对低度光滑函数和充分光滑函数,给出其数值差商公式的余项估计,然后推导出若干超收敛的数值差商公式并给出其余项的Lagrange表示.

关键词：公式差商数值 Lagrange 光滑函数余项估计超收敛

Some results on numerical divided difference formulas

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Science China Mathematics 2005年第11期48卷 1441-1450页

作者： Wang Xinghua,Wang Heyu & ming-jun lai Department of Mathematics, Zhejiang University, Hangzhou 310028, China Computing Center, Zhejiang University, Hangzhou 310012, China Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA Department of Mathematics Zhejiang University Hangzhou China Computing Center Zhejiang University Hangzhou China Department of Mathematics University of Georgia Athens USA

The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived wit... 详细信息

关键词： numerical divided difference remainder estimate functions of lower smoothness sufficiently smooth functions super convergence.

Flood management of Dongting Lake after operation of Three Gorges Dam

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Water Science and Engineering 2017年第4期10卷 303-310页

作者： Xi-jun lai Zi-ming Wang Key Laboratory of Watershed Geographic Sciences Nanjing Institute of Geography&LimnologyChinese Academy of Sciences(CAS)Nanjing 210008China Zhejiang Institute of Hydraulics and Estuary Hangzhou 310020Chin

Full operation of the Three Gorges Dam(TGD) reduces flood risk of the middle and lower parts of the Yangtze River Basin. However,Dongting Lake, which is located in the Yangtze River Basin, is still at high risk for potentially severe flooding in the future. The effects of the TGD on flood processes were investigated using a hydrodynamic model. The 1998 and 2010 flood events before and after the operation of the TGD, respectively, were analyzed. The numerical results show that the operation of the TGD changes flood processes, including the timing and magnitude of flood peaks in Dongting Lake. The TGD can effectively reduce the flood level in Dongting Lake, which is mainly caused by the flood water from the upper reach of the Yangtze River. This is not the case, however, for floods mainly induced by flood water from four main rivers in the catchment. In view of this, a comprehensive strategy for flood management in Dongting Lake is required. Non-engineering measures, such as warning systems and combined operation of the TGD and other reservoirs in the catchment, as well as traditional engineering measures, should be further improved. Meanwhile, a sustainable philosophy for flood control, including natural flood management and lake restoration, is recommended to reduce the flood risk.

关键词： Three Gorges Dam Flood control Water level Hydrodynamic model Dongting Lake

Persistent alterations in gray matter in COVID-19 patients experiencing sleep disturbances:a 3-month longitudinal study

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Neural Regeneration Research 2025年第10期20卷 3013-3024页

作者： Kaixuan Zhou Gaoxiong Duan Ying Liu Bei Peng Xiaoyan Zhou Lixia Qin Lingyan Liang Yichen Wei Qingping Zhang Xiaocheng Li Haixia Qin Yinqi lai Yian Lu Yan Zhang Jiazhu Huang Jinli Huang Yinfei Ouyang Bolin Bin mingming Zhao jun Liu Jianrong Yang Demao Deng Guangxi Key Laboratory of Special Biomedicine School of MedicineGuangxi UniversityNanningGuangxi Zhuang Autonomous RegionChina Department of Radiology the People’s Hospital of Guangxi Zhuang Autonomous RegionGuangxi Academy of Medical SciencesNanningGuangxi Zhuang Autonomous RegionChina Department of Sleep Medicine the People’s Hospital of Guangxi Zhuang Autonomous RegionNanningGuangxi Zhuang Autonomous RegionChina Department of Radiology The Second Xiangya HospitalCentral South UniversityChangshaHunan ProvinceChina Guangxi Clinical Research Center for Sleep Medicine the People’s Hospital of Guangxi Zhuang Autonomous RegionNanningGuangxi Zhuang Autonomous RegionChina

Sleep disturbances are among the most prevalent neuropsychiatric symptoms in individuals who have recovered from severe acute respiratory syndrome coronavirus 2 *** studies have demonstrated abnormal brain structures in patients with sleep disturbances who have recovered from coronavirus disease 2019(COVID-19).However,neuroimaging studies on sleep disturbances caused by COVID-19 are scarce,and existing studies have primarily focused on the long-term effects of the virus,with minimal acute phase *** a result,little is known about the pathophysiology of sleep disturbances in the acute phase of *** address this issue,we designed a longitudinal study to investigate whether alterations in brain structure occur during the acute phase of infection,and verified the results using 3-month follow-up data.A total of 26 COVID-19 patients with sleep disturbances(aged 51.5±13.57 years,8 women and 18 men),27 COVID-19 patients without sleep disturbances(aged 47.33±15.98 years,9 women and 18 men),and 31 age-and gender-matched healthy controls(aged 49.19±17.51 years,9 women and 22 men)were included in this *** COVID-19 patients with sleep disturbances were included in a longitudinal *** found that COVID-19 patients with sleep disturbances exhibited brain structural changes in almost all brain *** cortical thicknesses of the left pars opercularis and left precuneus were significantly negatively correlated with Pittsburgh Sleep Quality Index ***,we observed changes in the volume of the hippocampus and its subfield regions in COVID-19 patients compared with the healthy *** 3-month follow-up data revealed indices of altered cerebral structure(cortical thickness,cortical grey matter volume,and cortical surface area)in the frontal-parietal cortex compared with the baseline in COVID-19 patients with sleep *** findings indicate that the sleep disturbances patients had altered morphology in the cortical an

关键词： brain structure cortical gray matter volume cortical surface area cortical thickness hippocampus magnetic resonance imaging Pittsburgh Sleep Quality Index severe acute respiratory syndrome coronavirus 2 infections sleep disturbances sub-cortical volume

Soliton excitations and interaction in alpha helical protein with interspine coupling in modified nonlinear Schrodinger equation

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Chinese Physics B 2019年第12期28卷 130-135页

作者： ming-ming Li Cheng-lai Hu jun Wu Xian-Jing lai Yue-Yue Wang Zhejiang Provincial Key Laboratory of Chemical Utilization of Forestry Biomass School of SciencesZhejiang A&F UniversityHangzhou 311300China School of Humanity and Law Zhejiang A&F UniversityHangzhou 311300China College of Basic Science Zhejiang Shuren UniversityHangzhou 310015China

The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.

关键词： soliton three-coupling nonlinear modified Schrodinger equation similarity transformation

EFFECTS OF CONSOLIDATION TIME AND PARTICLE SIZE ON SCOUR RATES OF COHESIVE SEDIMENT

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Journal of Hydrodynamics 2007年第2期19卷 160-164页

作者： TAN Guang-ming WANG jun SHU Cai-wen lai Yong-hui State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan 430072 China

By means of flumes, experiments have been done in order to determine the effects of consolidation time and particle size on scour rates of cohesive sediment. Experimental results shown dry unit weight increased and scour rates decreased during the course of consolidation, the resistance to scour was related to consolidation time, but it presented different consolidation properties that depended on particle size. For the finer particle, the consolidation process was longer, the range of dry unit weight altered was greater, the consolidated sediments moved in chunks. On the other hand, based on analysis of the relationship of dry unit weight change with consolidation time, the simplified analytical expressions of dry unit weight and scour rates were derived, the results were checked with experimental data in the same flow situation and good agreements were achieved. Since the effects of different particle size were considered during the process of consolidation, the variations of consolidation properties were well reflected in these formulas.

关键词： cohesive sediment scour rates,consolidation time dry unit weight

Fast Transmission Photothermal Radiometry via Sampling by an Internal Computer Sound Card

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Journal of Electronic Science and Technology 2015年第1期13卷 73-77页

作者： lai-jun Yan Chun-ming Gao Bin-Xing Zhao Qi-ming Sun Feng Wang School of Optoelectronic Information University of Electronic Science and Technology of China

During the last few decades, photothermal radiometry（PTR） has been greatly developed and widely applied in the field of nondestructive testing. However, the traditional PTR system employs an expensive lock-in amplifier to detect the weak photothermal signal, which leads to high cost and long test time. In this paper, a fast transmission PTR system based on sampling by using an internal computer sound card was developed to lower the system cost and shorter the test time. A piece of amorphous silicon（a：Si） thin film solar cells with artificial defects was prepared and tested by the system. The results show that the sharpened defects can be identified easily and quickly according to the significant peaks of the original infrared signal sampled by the internal computer sound card. Furthermore, more detailed defects can be investigated by processing the infrared signal. These validate the effectiveness of the proposed transmission PTR system as a low cost and efficient non-destructive test technique.

关键词： Amorphous silicon thin film solar cells internal computer sound card nondestructive testing transmission photothermal radiometry