This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition f...This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.展开更多
A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical im...A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.展开更多
The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural p...The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.展开更多
Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-In...Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.展开更多
Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based comp...Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.展开更多
设H_(1),H_(2),H_(3)为无穷维复可分Hilbert空间,对给定关系A∈B CR(H_(1)),B∈B CR(H_(2)),C∈B CR(H_(3)),记M_(D,E,F):={A D E O B F O O C},其中D∈BR(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈BR(H_(3),H_(2))。得到了对任意D∈B(H_(2),...设H_(1),H_(2),H_(3)为无穷维复可分Hilbert空间,对给定关系A∈B CR(H_(1)),B∈B CR(H_(2)),C∈B CR(H_(3)),记M_(D,E,F):={A D E O B F O O C},其中D∈BR(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈BR(H_(3),H_(2))。得到了对任意D∈B(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈B(H_(3),H_(2))和D∈BR(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈B(H_(3),H_(2)),关系矩阵M_(D,E,F)都有闭值域的充分必要条件,并进一步刻画了两类3×3上三角关系矩阵的可能闭值域谱。展开更多
近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket...近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.展开更多
NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution ...NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution of these detectors,which detracts from an accurate analysis of the instrument spectra obtained,remains a crucial need.Based on the physical properties and spectrum formation processes of NaI(T1) scintillation detectors,the detector response to gamma photons with different energies is represented by photopeaks that are approximately Gaussian in shape with unique full-width-at-half-maximum(FWHM) values.The FWHM is established as a detector parameter based on resolution calibrations and is used in the construction of a general Gaussian response matrix,which is employed for the inverse decomposition of gamma spectra obtained from the detector.The Gold and Boosted Gold iterative algorithms are employed to accelerate the decomposition of the measured spectrum.Tests of the inverse decomposition method on multiple simulated overlapping peaks and on experimentally obtained U and Th radionuclide series spectra verify the practicability of the method,particularly in the low-energy region of the spectrum,providing for the accurate qualitative and quantitative analysis of radionuclides.展开更多
文摘This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.
文摘A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.
基金Quality Engineering Project of Anhui Province,China(No.2017zhkt036)
文摘The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.
基金Supported by the National Natural Science Foundation of China (No.60972039)Natural Science Foundation of Jiangsu Province (No.BK2007729)Natural Science Funding of Jiangsu Province (No.06KJA51001)
文摘Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.
基金National Natural Science Foundations of China(Nos.61201161,61271335)Postdoctoral Science Foundation of Jiangsu Province of China(No.1301002B)
文摘Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.
文摘设H_(1),H_(2),H_(3)为无穷维复可分Hilbert空间,对给定关系A∈B CR(H_(1)),B∈B CR(H_(2)),C∈B CR(H_(3)),记M_(D,E,F):={A D E O B F O O C},其中D∈BR(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈BR(H_(3),H_(2))。得到了对任意D∈B(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈B(H_(3),H_(2))和D∈BR(H_(2),H_(1)),E∈B(H_(3),H_(1)),F∈B(H_(3),H_(2)),关系矩阵M_(D,E,F)都有闭值域的充分必要条件,并进一步刻画了两类3×3上三角关系矩阵的可能闭值域谱。
文摘近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.
基金supported by the National Natural Science Foundation of China(Grant No.11365001)National Major Scientific Equipment Development Projects(Grant No.041514065)+2 种基金the Educational Commission of Jiangxi Province of China(Grant No.GJJ13464)Plan of Science and Technology of Jiangxi Province(Grant No.20141BBE50024)the Fundamental Science on Radioactive Geology and Exploration Technology Laboratory,East China Institute of Technology(Grant No.RGET1316)
文摘NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution of these detectors,which detracts from an accurate analysis of the instrument spectra obtained,remains a crucial need.Based on the physical properties and spectrum formation processes of NaI(T1) scintillation detectors,the detector response to gamma photons with different energies is represented by photopeaks that are approximately Gaussian in shape with unique full-width-at-half-maximum(FWHM) values.The FWHM is established as a detector parameter based on resolution calibrations and is used in the construction of a general Gaussian response matrix,which is employed for the inverse decomposition of gamma spectra obtained from the detector.The Gold and Boosted Gold iterative algorithms are employed to accelerate the decomposition of the measured spectrum.Tests of the inverse decomposition method on multiple simulated overlapping peaks and on experimentally obtained U and Th radionuclide series spectra verify the practicability of the method,particularly in the low-energy region of the spectrum,providing for the accurate qualitative and quantitative analysis of radionuclides.
