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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
文摘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.
基金the National Natural Science Foundation of China(Grant No.11771099)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716,15300717)supported by the Innovation Program of Shanghai Municipal Education Commission。
文摘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.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2016R1D1A1B03931529)。
文摘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.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2018R1A6A3A11043447,to HDL)。
文摘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.
基金Clinical Research Fostering Fund of Chinese PLA General Hospital in China,No.2017FC-TSYS-2012(to FYL)Youth Program of the Natural Science Foundation of Hainan Province of China,No.819QN378(to FYL)+2 种基金the National Natural Science Foundation of China,No.81771481(to XLC)China National Key R&D Program,No.2018YFC1312602(to XLC)National Clinical Research Center for Geriatric Diseases of China,No.NCRCGPLAGH-2017007(to XLC)。
文摘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.
基金Magnetic Laboratory Visiting Scientist Program,Grant/Award Number 327Chicago Biomedical Consortium,Grant/Award Number 085740National Science Foundation,Grant/Award Number DMR-1157490。
文摘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.
基金Supported by NSFC(Grant No.11471077)the Scientific Research Fund of Fujian Provincial Education Department(Grant No.JAT191106)。
文摘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.
基金supported by the National Natural Science Foundation of China,No.11672332 (to XYC)the National Key Research and Development Plan of China,No.2016YFC1101500 (to SZ).
文摘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).
基金supported by NSFC 11971415Nanhu Scholars Program for Young Scholars of XYNU.
文摘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.
基金National Natural Science Foundation of China (Grant No. 11701356)supported by National Natural Science Foundation of China (Grant No. 11571234)+2 种基金supported by National Natural Science Foundation of China (Grant No. 11571220)National Postdoctoral Program for Innovative Talents (Grant No. BX201600097)China Postdoctoral Science Foundation (Grant No. 2016M601562)。
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11575120 and 11822504)JSPS KAKENHI(No.JP19K03858).
文摘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.
基金Aerospace Power Foundation(6141B09050397)Foudamental Reasearch Foundation of North China University of Technology(110052971921/042).
文摘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.
基金Supported in part by the National Natural Science Foundation of China(11975116,11665016,11563006)Jiangxi Science Foundation for Distinguished Young Scientists(20192BCB23007)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grants No.U1832120 and No.11675265)the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China(Grant No.A2018210146)the Continuous Basic Scientific Research Project(Grant No.WDJC-2019-13).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61701507,61890542,and 61890540).
文摘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.