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A Global Rigidity Theorem for the Length of Concircular Curvature Tensor on the Locally Conformally Symmetric Riemannian Manifold 认领
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作者 Shipei HU 《数学研究及应用:英文版》 CSCD 2020年第2期187-195,共9页
In this paper, we study the locally conformally symmetric closed Riemannian manifold, and establish a global rigidity theorem for the length of the concircular curvature vector.
关键词 conformally SYMMETRIC RIEMANNIAN CURVATURE TENSOR concircular CURVATURE vector WEYL TENSOR Schouten TENSOR
M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds 认领
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作者 Yun Miao Liqun Qi Yimin Wei 《数学研究通讯:英文版》 CSCD 2020年第3期336-353,共18页
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-e... We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity. 展开更多
关键词 M-eigenvalue Riemann curvature tensor Ricci tensor conformal invariant canonical form
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定向超图逆Perron值的若干上界 认领
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作者 汪乐 徐静 《信阳农林学院学报》 2020年第2期114-116,126,共4页
定向超图是一个带有点-边关联定向的超图。基于定向超图邻接张量和拉普拉斯张量的定义给出了定向超图逆Perron值和逆Perron向量。利用定向超图的顶点数、边数、度序列和逆Perron向量刻画了定向超图逆Perron值的若干上界。
关键词 定向超图 张量 拉普拉斯张量 逆Perron值
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一种基于张量的车辆交通数据缺失估计新方法 认领
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作者 张德干 范洪瑞 +4 位作者 龚倡乐 高瑾馨 张婷 赵彭真 陈晨 《计算机科学》 CSCD 北大核心 2020年第S01期505-511,共7页
面对当前庞大的智慧交通数据量,收集并统计处理是必要且重要的过程,但无法避免的数据缺失问题是目前的研究重点。文中针对车辆交通数据缺失问题提出一种基于张量的车辆交通数据缺失估计新方法:集成贝叶斯张量分解(Integrated Bayesian T... 面对当前庞大的智慧交通数据量,收集并统计处理是必要且重要的过程,但无法避免的数据缺失问题是目前的研究重点。文中针对车辆交通数据缺失问题提出一种基于张量的车辆交通数据缺失估计新方法:集成贝叶斯张量分解(Integrated Bayesian Tensor Decomposition,IBTD)。该算法在数据模型构建阶段,利用随机采样原理,将缺失数据随机抽取生成数据子集,并用优化后的贝叶斯张量分解算法进行插补。引入集成思想,将多个插补后的误差结果进行分析排序,考虑时空复杂度,择优平均得到最优结果。通过平均绝对百分比误差之后(Mean Absolute Percentage Error,MAPE)和均方根误差(Root Mean Square Error,RMSE)对提出模型的性能进行评估。实验结果表明,所提新方法能够有效地对不同缺失量的交通数据集进行插补,并能得到很好的插补结果。 展开更多
关键词 交通数据 数据缺失 张量 随机采样 贝叶斯张量分解
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Multi-Aspect Incremental Tensor Decomposition Based on Distributed In-Memory Big Data Systems 认领
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作者 Hye-Kyung Yang Hwan-Seung Yong 《数据与情报科学学报:英文版》 CSCD 2020年第2期13-32,共20页
Purpose:We propose In Par Ten2,a multi-aspect parallel factor analysis three-dimensional tensor decomposition algorithm based on the Apache Spark framework.The proposed method reduces re-decomposition cost and can han... Purpose:We propose In Par Ten2,a multi-aspect parallel factor analysis three-dimensional tensor decomposition algorithm based on the Apache Spark framework.The proposed method reduces re-decomposition cost and can handle large tensors.Design/methodology/approach:Considering that tensor addition increases the size of a given tensor along all axes,the proposed method decomposes incoming tensors using existing decomposition results without generating sub-tensors.Additionally,In Par Ten2 avoids the calculation of Khari–Rao products and minimizes shuffling by using the Apache Spark platform.Findings:The performance of In Par Ten2 is evaluated by comparing its execution time and accuracy with those of existing distributed tensor decomposition methods on various datasets.The results confirm that In Par Ten2 can process large tensors and reduce the re-calculation cost of tensor decomposition.Consequently,the proposed method is faster than existing tensor decomposition algorithms and can significantly reduce re-decomposition cost.Research limitations:There are several Hadoop-based distributed tensor decomposition algorithms as well as MATLAB-based decomposition methods.However,the former require longer iteration time,and therefore their execution time cannot be compared with that of Spark-based algorithms,whereas the latter run on a single machine,thus limiting their ability to handle large data.Practical implications:The proposed algorithm can reduce re-decomposition cost when tensors are added to a given tensor by decomposing them based on existing decomposition results without re-decomposing the entire tensor.Originality/value:The proposed method can handle large tensors and is fast within the limited-memory framework of Apache Spark.Moreover,In Par Ten2 can handle static as well as incremental tensor decomposition. 展开更多
关键词 PARAFAC Tensor decomposition Incremental tensor decomposition Apache Spark Big data
Injury of the dentatorubrothalamic tract in patients with post-traumatic tremor following mild traumatic brain injury: a case-control study 认领
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作者 Sung Ho Jang Han Do Lee 《中国神经再生研究:英文版》 SCIE CAS CSCD 2020年第11期2063-2066,共4页
Post-traumatic movement disorder is one of the sequelae of traumatic brain injury. The dentatorubrothalamic tract(DRTT) is reported to be involved in the control of movement. Therefore, injury of the DRTT can be accom... Post-traumatic movement disorder is one of the sequelae of traumatic brain injury. The dentatorubrothalamic tract(DRTT) is reported to be involved in the control of movement. Therefore, injury of the DRTT can be accompanied by abnormal movements, including ataxia, tremor, or dystonia. We investigated DRTT injuries in 27 patients who showed post-traumatic tremor in at least one of four extremities following mild traumatic brain injury. We classified DRTT injuries based on diffusion tensor tractography parameters and configuration: type A: the DRTT showed narrowing, type B: the DRTT showed partial tearing, and type C: the DRTT showed discontinuation. Fractional anisotropy and fiber number of the DRTT were significantly decreased in patients compared with the healthy controls. Based on our DRTT injury classification, among the 54 hemispheres of the 27 patients, type A injury occurred in 22 hemispheres(40.7%) of 17 patients, type B injury was present in 15 hemispheres(27.7%) of 10 patients, and type C injury was observed in 8 hemispheres(14.8%) of 6 patients. Our results suggest that diffusion tensor tractography-based evaluation of the DRTT would be useful when determining cause of post-traumatic tremor in patients with mild traumatic brain injury. The study protocol was approved by the Institutional Review Board of Yeungnam University Hospital(YUMC-2018-09-007) on September 5, 2018. 展开更多
关键词 dentatorubrothalamic TRACT DIFFUSION TENSOR imaging DIFFUSION TENSOR tractography fiber number fractional anisotropy mild traumatic brain INJURY POST-TRAUMATIC TREMOR region of interest
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文章速递Identification of risk factors for poor language outcome in surgical resection of glioma involving the arcuate fasciculus:an observational study 认领
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作者 Fang-Ye Li Hong-Yu Liu +6 位作者 Jun Zhang Zheng-Hui Sun Jia-Shu Zhang Guo-Chen Sun Xin-Guang Yu Xiao-Lei Chen Bai-Nan Xu 《中国神经再生研究:英文版》 SCIE CAS CSCD 2021年第2期333-337,共5页
The arcuate fasciculus is a critical component of the neural substrate of human language function.Surgical resection of glioma adjacent to the arcuate fasciculus likely damages this region.In this study,we evaluated t... The arcuate fasciculus is a critical component of the neural substrate of human language function.Surgical resection of glioma adjacent to the arcuate fasciculus likely damages this region.In this study,we evaluated the outcome of surgical resection of glioma adjacent to the arcuate fasciculus under the guidance of magnetic resonance imaging and diffusion tensor imaging,and we aimed to identify the risk factors for postoperative linguistic deficit.In total,54 patients with primary glioma adjacent to the arcuate fasciculus were included in this observational study.These patients comprised 38 men and 16 women(aged 43±11 years).All patients underwent surgical resenction of glioma under the guidance of magnetic resonance imaging and diffusion tensor imaging.Intraoperative images were updated when necessary for further resection.The gross total resection rate of the 54 patients increased from 38.9%to 70.4%by intraoperative magnetic resonance imaging.Preoperative language function and glioma-to-arcuate fasciculus distance were associated with poor language outcome.Multivariable logistic regression analyses showed that glioma-to-arcuate fasciculus distance was the major independent risk factor for poor outcome.The cutoff point of glioma-to-arcuate fasciculus distance for poor outcome was 3.2 mm.These findings suggest that intraoperative magnetic resonance imaging combined with diffusion tensor imaging of the arcuate fasciculus can help optimize tumor resection and result in the least damage to the arcuate fasciculus.Notably,glioma-to-arcuate fasciculus distance is a key independent risk factor for poor postoperative language outcome.This study was approved by the Ethics Committee of the Chinese PLA General Hospital,China(approval No.S2014-096-01)on October 11,2014. 展开更多
关键词 arcuate fasciculus central nervous system brain diffusion tensor imaging intraoperative magnetic resonance imaging language function risk factor trial
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相对论中的若干“勾股定理” 认领
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作者 周国全 《大学物理》 2020年第5期10-13,共4页
本文总结了作者讲授电动力学与狭义相对论的若干心得与体会;运用四维闵可夫斯基空间张量的性质及其缩并运算法则,介绍了用各阶四维张量构造相对论不变量即四维标量的方法,进而在所得四维标量为负定的类时标量时,推导出若干典型的勾股关... 本文总结了作者讲授电动力学与狭义相对论的若干心得与体会;运用四维闵可夫斯基空间张量的性质及其缩并运算法则,介绍了用各阶四维张量构造相对论不变量即四维标量的方法,进而在所得四维标量为负定的类时标量时,推导出若干典型的勾股关系,并应用或验证于若干简单情形. 展开更多
关键词 狭义相对论 张量 相对论不变量 勾股定理 四维闵可夫斯基空间 洛伦兹变换
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Assessing neuraxial microstructural changes in a transgenic mouse model of early stage Amyotrophic Lateral Sclerosis by ultra-high field MRI and diffusion tensor metrics 认领
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作者 Rodolfo G.Gatto Carina Weissmann +5 位作者 Manish Amin Ariel Finkielsztein Ronen Sumagin Thomas H.Mareci Osvaldo D.Uchitel Richard L.Magin 《动物模型与实验医学(英文)》 CSCD 2020年第2期117-129,共13页
Objective: Cell structural changes are one of the main features observed during the development of amyotrophic lateral sclerosis(ALS). In this work, we propose the use of diffusion tensor imaging(DTI) metrics to asses... Objective: Cell structural changes are one of the main features observed during the development of amyotrophic lateral sclerosis(ALS). In this work, we propose the use of diffusion tensor imaging(DTI) metrics to assess specific ultrastructural changes in the central nervous system during the early neurodegenerative stages of ALS.Methods: Ultra-high field MRI and DTI data at 17.6 T were obtained from fixed, excised mouse brains, and spinal cords from ALS(G93 A-SOD1) mice.Results: Changes in fractional anisotropy(FA) and linear, planar, and spherical anisotropy ratios(C_L, C_P, and C_S, respectively) of the diffusion eigenvalues were measured in white matter(WM) and gray matter(GM) areas associated with early axonal degenerative processes(in both the brain and the spinal cord). Specifically, in WM structures(corpus callosum, corticospinal tract, and spinal cord funiculi) as the disease progressed, FA, C_L, and C_P values decreased, whereas C_S values increased. In GM structures(prefrontal cortex, hippocampus, and central spinal cord) FA and C_P decreased, whereas the C_L and C_S values were unchanged or slightly smaller. Histological studies of a fluorescent mice model(YFP, G93 A-SOD1 mouse) corroborated the early alterations in neuronal morphology and axonal connectivity measured by DTI.Conclusions: Changes in diffusion tensor shape were observed in this animal model at the early, nonsymptomatic stages of ALS. Further studies of C_L, C_P, and C_S as imaging biomarkers should be undertaken to refine this neuroimaging tool for future clinical use in the detection of the early stages of ALS. 展开更多
关键词 amyotrophic lateral sclerosis animal models diffusion tensor imaging G93A-SOD1 mice ultra-high field MRI
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On the α-spectra of Uniform Hypergraphs and Its Associated Graphs 认领
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作者 Yuan HOU An CHANG Chao SHI 《数学学报:英文版》 SCIE CSCD 2020年第7期842-850,共9页
For 0 ≤α < 1 and a k-uniform hypergraph H, the tensor Aα(H) associated with H is defined as Aα(H) = αD(H) +(1-α)A(H), where D(H) and A(H) are the diagonal tensor of degrees and the adjacency tensor of H, resp... For 0 ≤α < 1 and a k-uniform hypergraph H, the tensor Aα(H) associated with H is defined as Aα(H) = αD(H) +(1-α)A(H), where D(H) and A(H) are the diagonal tensor of degrees and the adjacency tensor of H, respectively. The α-spectra of H is the set of all eigenvalues of Aα(H) and the α-spectral radius ρα(H) is the largest modulus of the elements in the spectrum of Aα(H). In this paper we define the line graph L(H) of a uniform hypergraph H and prove that ρα(H) ≤■ρα(L(H)) + 1 + α(Δ-1-δ*/k), where Δ and δ* are the maximum degree of H and the minimum degree of L(H), respectively. We also generalize some results on α-spectra of Gk,s, which is obtained from G by blowing up each vertex into an s-set and each edge into a k-set where 1 ≤ s ≤ k/2. 展开更多
关键词 TENSOR SPECTRA UNIFORM
Three-dimensional bioprinting collagen/silk fibroin scaffold combined with neural stem cells promotes nerve regeneration after spinal cord injury 认领
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作者 Ji-Peng Jiang Xiao-Yin Liu +9 位作者 Fei Zhao Xiang Zhu Xiao-Yin Li Xue-Gang Niu Zi-Tong Yao Chen Dai Hui-You Xu Ke Ma Xu-Yi Chen Sai Zhang 《中国神经再生研究:英文版》 SCIE CAS CSCD 2020年第5期959-968,共10页
Many studies have shown that bio-scaffolds have important value for promoting axonal regeneration of injured spinal cord.Indeed,cell transplantation and bio-scaffold implantation are considered to be effective methods... Many studies have shown that bio-scaffolds have important value for promoting axonal regeneration of injured spinal cord.Indeed,cell transplantation and bio-scaffold implantation are considered to be effective methods for neural regeneration.This study was designed to fabricate a type of three-dimensional collagen/silk fibroin scaffold (3D-CF) with cavities that simulate the anatomy of normal spinal cord.This scaffold allows cell growth in vitro and in vivo.To observe the effects of combined transplantation of neural stem cells (NSCs) and 3D-CF on the repair of spinal cord injury.Forty Sprague-Dawley rats were divided into four groups: sham (only laminectomy was performed),spinal cord injury (transection injury of T10 spinal cord without any transplantation),3D-CF (3D scaffold was transplanted into the local injured cavity),and 3D-CF + NSCs (3D scaffold co-cultured with NSCs was transplanted into the local injured cavity.Neuroelectrophysiology,imaging,hematoxylin-eosin staining,argentaffin staining,immunofluorescence staining,and western blot assay were performed.Apart from the sham group,neurological scores were significantly higher in the 3D-CF + NSCs group compared with other groups.Moreover,latency of the 3D-CF + NSCs group was significantly reduced,while the amplitude was significantly increased in motor evoked potential tests.The results of magnetic resonance imaging and diffusion tensor imaging showed that both spinal cord continuity and the filling of injury cavity were the best in the 3D-CF + NSCs group.Moreover,regenerative axons were abundant and glial scarring was reduced in the 3D-CF + NSCs group compared with other groups.These results confirm that implantation of 3D-CF combined with NSCs can promote the repair of injured spinal cord.This study was approved by the Institutional Animal Care and Use Committee of People’s Armed Police Force Medical Center in 2017 (approval No.2017-0007.2). 展开更多
关键词 3D BIOPRINTING COLLAGEN diffusion tensor IMAGING functional recovery magnetic resonance IMAGING nerve REGENERATION NEURAL REGENERATION NEURAL stem cell SCAFFOLD silk fibroin spinal cord injury
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Gradient Estimates for a Nonlinear Heat Equation Under Finsler-geometric Flow 认领
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作者 ZENG Fanqi 《偏微分方程:英文版》 CSCD 2020年第1期17-38,共22页
This paper considers a compact Finsler manifold(Mn,F(t),m)evolving under a Finsler-geometric flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation(a)tu(x,t)=△m... This paper considers a compact Finsler manifold(Mn,F(t),m)evolving under a Finsler-geometric flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation(a)tu(x,t)=△mu(x,t),(x,t)∈M×[0,T],where△m is the Finsler-Laplacian.By integrating the gradient estimates,we derive the corresponding Harnack inequalities.Our results generalize and correct the work of S.Lakzian,who established similar results for the Finsler-Ricci flow.Our results are also natural extension of similar results on Riemannian-geometric flow,previously studied by J.Sun.Finally,we give an application to the Finsler-Yamabe flow. 展开更多
关键词 Gradient estimate nonlinear heat equation Harnack inequality Akbarzadeh's Ricci tensor Finsler-geometric flow
Completely positive tensors in the complex field 认领
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作者 Anwa Zhou Jinyan Fan Qingwen Wang 《中国科学:数学英文版》 SCIE CSCD 2020年第6期1219-1234,共16页
In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the... In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained. 展开更多
关键词 complex completely positive tensor complex completely positive decomposition truncated moment problem semidefinite program
Contributions of optimized tensor interactions on the binding energies of nuclei 认领
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作者 Di Wu Chun-Lin Bai +2 位作者 H.Sagawa Zeng-Qiang Song Huan-Qiao Zhang 《核技术:英文版》 SCIE CAS CSCD 2020年第2期11-19,共9页
The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting ... The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting between proton h11=2 and g7=2 single-particle orbits along the Z=50 isotopes.With the optimized tensor interactions,the binding energies of spherical or weakly deformed nuclei with A=54-228 are studied systematically.The present results show that the global effect of tensor interaction is attractive and systematically increases the binding energies of all these nuclei and makes the nuclei more bound.The root mean squared deviation of the calculated binding energies from the experimental values is significantly improved by the optimized tensor interactions,and the contribution of the tensor interaction to the binding energy is estimated. 展开更多
关键词 TENSOR force Binding ENERGY GAMOW-TELLER TRANSITION Spin-dipole TRANSITION SINGLE-PARTICLE ENERGY differences
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Numerical study of transonic separation flow using an anisotropic turbulence model 认领
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作者 YAN Wenhui PENG Tengfei +2 位作者 YONG Yan QIN Ruixin MA Ruige 《航空动力学报》 EI CAS CSCD 北大核心 2020年第1期114-125,共12页
A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied,when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-inter... A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied,when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-interaction(SWBLI).To capture the essential behavior of this complex flow,the current study utilized an anisotropic turbulence model developed on the basis of a statistical partial average scheme.The first order moment of turbulent fluctuations,retained by a novel average scheme,and the turbulent length scale,can be determined from the momentum equations and mechanical energy equation of the fluctuation flow,respectively.The two physical quantities were readily used to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve the computational results.Comparisons between the computational results and experimental data were carried out for velocity profiles,pressure distribution,skin friction coefficient,Reynolds stress as well as streamline vectors distribution.Without using any empirical coefficients and wall functions,the numerical results were in good agreement with the available experimental data,further confirming that the nonlinear anisotropic eddy viscosity tensor is the decisive factor for the success of the computational results. 展开更多
关键词 TRANSONIC SEPARATION FLOW EDDY viscosity TENSOR shock wave boundary layer interaction ANISOTROPIC turbulence model statistical partial average scheme
Quantum bit threads of MERA tensor network in large c limit 认领
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作者 陈崇斌 舒富文 吴孟和 《中国物理C:英文版》 SCIE CAS CSCD 2020年第7期184-198,共15页
The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is... The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow. 展开更多
关键词 gauge-gravity duality holographic entanglement entropy tensor network
Nuclear properties of Z=114 isotopes and shell structure of^298114 认领
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作者 王艳召 高永浩 +1 位作者 崔建坡 顾建中 《理论物理通讯:英文版》 SCIE CAS CSCD 2020年第2期75-82,共8页
The two-neutron separation energies(S2n)andα-decay energies(Qα)of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB)approach with the SLy5,T22,T32 and T43 interactions.It is found... The two-neutron separation energies(S2n)andα-decay energies(Qα)of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB)approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S2n and Qαevolutions with neutron number N.Meanwhile,the single-particle energy spectra of 298114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus 298114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of 298114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force. 展开更多
关键词 SUPERHEAVY nuclei Skyrme–Hartree–Fock–Bogoliubov approach tensor force two-neutron separation ENERGIES ALPHA-DECAY ENERGIES shell structure PSEUDOSPIN symmetry
各向异性磁介质边值关系的具体坐标形式 认领
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作者 李文略 《曲阜师范大学学报:自然科学版》 CAS 2020年第2期72-78,共7页
陈燊年(2012)由各向异性磁介质的性质方程出发,推导出用张量方程表示的各向异性磁介质的边值关系.张量方程的协变性是边值关系在不同坐标系中的具体坐标形式相互转换的数理依据.由张量方程的协变性,应用张量分析的矩阵方法推导出边值关... 陈燊年(2012)由各向异性磁介质的性质方程出发,推导出用张量方程表示的各向异性磁介质的边值关系.张量方程的协变性是边值关系在不同坐标系中的具体坐标形式相互转换的数理依据.由张量方程的协变性,应用张量分析的矩阵方法推导出边值关系在空间直角坐标系和磁各向异性球坐标系下的具体坐标形式.推导的过程以及所得结果有助于加深对各向异性磁介质磁导属性的理解.对各向异性磁导率常数作适当的处理,所得的边值关系适用于各向同性磁介质. 展开更多
关键词 各向异性磁介质 边值条件 张量 矩阵
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求解张量分裂可行问题的半定松弛法 认领
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作者 金雨轩 徐旭冬 赵金玲 《河南科技大学学报:自然科学版》 CAS 北大核心 2020年第1期80-85,M0007,M0008共8页
投影法是求解分裂可行问题的传统方法,但投影法的求解效率依赖于初始点的选择,且无法直接应用于张量分裂可行问题。本文提出了利用半定松弛法来求解一类特殊的张量分裂可行问题。假设问题中集合的形式由多项式不等式给出,则可将张量分... 投影法是求解分裂可行问题的传统方法,但投影法的求解效率依赖于初始点的选择,且无法直接应用于张量分裂可行问题。本文提出了利用半定松弛法来求解一类特殊的张量分裂可行问题。假设问题中集合的形式由多项式不等式给出,则可将张量分裂可行问题松弛化为半定规划问题,再应用半定松弛法求解。本文给出了半定松弛法的相关原理,并进行了数值实验。实验结果表明:对于集合取不同范围、张量中的元素取不同值、张量取不同维数和不同阶数,该松弛化方法都能够用于求解张量分裂可行问题。 展开更多
关键词 张量 分裂可行问题 半定松弛 半定规划 多项式
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Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar 认领
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作者 谢前朋 潘小义 肖顺平 《中国物理B:英文版》 SCIE EI CAS CSCD 2020年第5期333-345,共13页
An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing ... An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator. 展开更多
关键词 colocated coprime MIMO radar noncircular signal tensor decomposition DOD and DOA estimation
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