In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） al...In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.展开更多
A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, ...A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.展开更多
The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identica...The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.展开更多
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruenc...In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.展开更多
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and...A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and a method of [GRAPHICS] diagonalization of matrices over quaternion field is given.展开更多
User selection is necessary for multiuser multiple-input multiple-output(MIMO) downlink systems with block diagonalization(BD) due to the limited free spatial transmit dimensions.The pure user selection algorithms can...User selection is necessary for multiuser multiple-input multiple-output(MIMO) downlink systems with block diagonalization(BD) due to the limited free spatial transmit dimensions.The pure user selection algorithms can be improved by performing receive antenna selection(RAS) to increase sum rate.In this paper,a joint user and antenna selection algorithm,which performs user selection for sum rate maximization in the first stage and then performs antenna selection in the second stage,is proposed.The antenna selection process alternately drops one antenna with the poorest channel quality based on maximum determinant ranking(MDR) from the users selected during the first stage and activates one antenna with the maximum norm of projected channel from the remaining users.Simulation results show that the proposed algorithm significantly outperforms the algorithm only performing user selection as well as the algorithm combining user selection with MDR receive antenna selection in terms of sum rate.展开更多
In this paper, we study the performance of block diagonalization (BD) scheme for a downlink multiuser multi-input multi-output (MIMO) system with imperfect channel state information (CSI). At each mobile user, informa...In this paper, we study the performance of block diagonalization (BD) scheme for a downlink multiuser multi-input multi-output (MIMO) system with imperfect channel state information (CSI). At each mobile user, information about the channel is obtained by applying the minimum mean-square-error (MMSE) channel estimation method. The channel state information is fed back to the base station through error-free uplink channels. A theoretical analysis is performed showing that channel estimation errors contribute to co-channel interferences thus deteriorating sum rate capacity. Computer simulations are performed to evaluate the impact of channel estimation errors on the sum rate capacity. The results show that if the MSE of the channel estimation is not less than 10-2, the impact of channel estimation errors is significant and cannot be neglected. To combat this adverse effect, a proper transmit power level is required for the training signals.展开更多
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic be...In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.展开更多
In this paper, we propose a two-dimensional （2-D） angles of arrival （AOAs） estimation method based on a joint diagonalization of two spatio-temporal （ST） correlation matrices. The mathematical manipulations prop...In this paper, we propose a two-dimensional （2-D） angles of arrival （AOAs） estimation method based on a joint diagonalization of two spatio-temporal （ST） correlation matrices. The mathematical manipulations proposed in this paper take the structure of the array that enable estimating 2-D AOAs simultaneously without 2-D searching or pairing. The performance comparison shows that the proposed method is better than ST-DOA matrix method.展开更多
We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimen...We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.展开更多
A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new...A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching. Moreover, it can handle sources with common 1-D angles. Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method, especially for low signal-to-noise ratio case.展开更多
A novel joint diagonalization （DOA） matrix method is proposed to estimate the two-dimensional （2-D） DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structur...A novel joint diagonalization （DOA） matrix method is proposed to estimate the two-dimensional （2-D） DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structure of the array, thereby obtaining the 2-D DOAs of the array based on joint diagonalization directly with neither peak search nor pair matching. The new method can handle sources with common 1-D angles. Simulation results show the effectiveness of the method.展开更多
Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<...Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<sub>2k</sub><sup>n</sup>ew（N）⊕S<sub>2k</sub><sup>o</sup>ld（N）and there exists a basis in S<sub>2k</sub><sup>n</sup>ew（N） which are eigenvectors for all Hecke operators but there exists a basis in S<sub>2k</sub><sup>o</sup>ld（N） which are eigenvectors for only those Hecke operators T（p）((p,展开更多
The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. This paper describes a relative gradient non-orthogonal approximate joint d...The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. This paper describes a relative gradient non-orthogonal approximate joint diagonalization （AJD） algorithm based on a non-least squares AJD criterion and a special AJD using a non-square diagonalizing matrix and an AJD method for ill-conditioned matrices. Simulation results demonstrate the better performance of the relative gradient AJD algorithm compared with the conventional least squares （LS） criteria based gradient-type AJD algorithms. The algorithm is attractive for practical applications since it is simple and efficient.展开更多
In multi-cell cooperative multi-input multi-output （MIMO） systems, base station （BS） can exchange and utilize channel state information （CSI） of adjacent cell users to manage co-channel interference. Users quant...In multi-cell cooperative multi-input multi-output （MIMO） systems, base station （BS） can exchange and utilize channel state information （CSI） of adjacent cell users to manage co-channel interference. Users quantize the CSIs of desired channel and interference channels using finite-rate feedback links, then BS can generate cooperative block diagonalization （BD） precoding matrices using the obtained quantized CSI at transmitter to supress co-channel interference. In this paper, a novel adaptive bit allocation scheme is proposed to minimize the rate loss due to imperfect CSI. We derive the closed-form expression of rate loss caused by both channel delay and limited feedback. Based on the derived rate loss expression, the proposed scheme can adaptively allocate more bits to quantize the better channels with smaller delays and fewer bits to worse channels with larger delays. Simulation results show that the proposed scheme yields higher performance than other allocation schemes.展开更多
Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One...Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges,which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects.This,in turn,generates many intriguing field-induced novel phases and the thermal Hall effect.In this review,we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′exchange from a numerical perspective.The review discusses certain representative exotic phases such as𝛤spin liquid,nematic ferromagnet,spin-flop phase,and distinct chiral spin states with spontaneous time-reversal symmetry breaking.It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.展开更多
Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numeri...Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numerical characterizations and similarity analysis of sequences. Initially, a transformation method was introduced to represent each DNA sequence with dinucleotide physicochemical property matrix. Then, based on the approximate joint diagonalization theory, an eigenvalue vector was extracted from each DNA sequence,which could be considered as descriptor of the DNA sequence. Moreover, similarity analyses were performed by calculating the pair-wise distances among the obtained eigenvalue vectors. The results show that the proposed approach can capture more sequence information, and can jointly analyze the information contained in all involved multiple sequences, rather than separately, whose effectiveness was demonstrated intuitively by constructing a dendrogram for the 15 beta-globin gene sequences.展开更多
基金supported by the National Natural Science Foundation of China(6167145361201379)Anhui Natural Science Foundation of China(1608085MF123)
文摘In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.
基金supported partly by the Key Program of National Natural Science Foundation of China (U0635001U0835003)+3 种基金the National Natural Science Foundation of China (60505005 60674033 60774094)the Natural Science Fundof Guangdong Province (05006508).
文摘A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.
文摘The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘A concept of [GRAPHICS] diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a [GRAPHICS] diagonalization one are discussed, and a method of [GRAPHICS] diagonalization of matrices over quaternion field is given.
基金the National Science and Technology Major Project (No.2009ZX03002-003)
文摘User selection is necessary for multiuser multiple-input multiple-output(MIMO) downlink systems with block diagonalization(BD) due to the limited free spatial transmit dimensions.The pure user selection algorithms can be improved by performing receive antenna selection(RAS) to increase sum rate.In this paper,a joint user and antenna selection algorithm,which performs user selection for sum rate maximization in the first stage and then performs antenna selection in the second stage,is proposed.The antenna selection process alternately drops one antenna with the poorest channel quality based on maximum determinant ranking(MDR) from the users selected during the first stage and activates one antenna with the maximum norm of projected channel from the remaining users.Simulation results show that the proposed algorithm significantly outperforms the algorithm only performing user selection as well as the algorithm combining user selection with MDR receive antenna selection in terms of sum rate.
文摘In this paper, we study the performance of block diagonalization (BD) scheme for a downlink multiuser multi-input multi-output (MIMO) system with imperfect channel state information (CSI). At each mobile user, information about the channel is obtained by applying the minimum mean-square-error (MMSE) channel estimation method. The channel state information is fed back to the base station through error-free uplink channels. A theoretical analysis is performed showing that channel estimation errors contribute to co-channel interferences thus deteriorating sum rate capacity. Computer simulations are performed to evaluate the impact of channel estimation errors on the sum rate capacity. The results show that if the MSE of the channel estimation is not less than 10-2, the impact of channel estimation errors is significant and cannot be neglected. To combat this adverse effect, a proper transmit power level is required for the training signals.
文摘In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.
基金This work was supported the National Natural Science Foundation of China under Grand No.60372022the Program for New Century Excellent Talents in University under Grand No. NCET-05-0806.
文摘In this paper, we propose a two-dimensional （2-D） angles of arrival （AOAs） estimation method based on a joint diagonalization of two spatio-temporal （ST） correlation matrices. The mathematical manipulations proposed in this paper take the structure of the array that enable estimating 2-D AOAs simultaneously without 2-D searching or pairing. The performance comparison shows that the proposed method is better than ST-DOA matrix method.
基金supported by the National Key Projects for Research and Development of China(Grant Nos.2021YFA1400400 and 2024YFA1408104)the National Natural Science Foundation of China(Grant Nos.12434005,12374137,and 92165205).
文摘We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
基金the National Natural Science Foundation of China (Grant No.60372022)Program for New Century Excellent Talents in University (Grant No.NCET-05-0806)
文摘A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching. Moreover, it can handle sources with common 1-D angles. Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method, especially for low signal-to-noise ratio case.
基金Supported by the National Natural Science Foundation of China (Grant No. 60372022)Program for New Century Excellent Talents in University (Grand No. NCET-05-0806)
文摘A novel joint diagonalization （DOA） matrix method is proposed to estimate the two-dimensional （2-D） DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structure of the array, thereby obtaining the 2-D DOAs of the array based on joint diagonalization directly with neither peak search nor pair matching. The new method can handle sources with common 1-D angles. Simulation results show the effectiveness of the method.
文摘Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<sub>2k</sub><sup>n</sup>ew（N）⊕S<sub>2k</sub><sup>o</sup>ld（N）and there exists a basis in S<sub>2k</sub><sup>n</sup>ew（N） which are eigenvectors for all Hecke operators but there exists a basis in S<sub>2k</sub><sup>o</sup>ld（N） which are eigenvectors for only those Hecke operators T（p）((p,
基金Supported by the Basic Research Foundation of Tsinghua National Laboratory for Information Science and Technology (TNList) the National Natural Science Foundation of China (No. 60675002)
文摘The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. This paper describes a relative gradient non-orthogonal approximate joint diagonalization （AJD） algorithm based on a non-least squares AJD criterion and a special AJD using a non-square diagonalizing matrix and an AJD method for ill-conditioned matrices. Simulation results demonstrate the better performance of the relative gradient AJD algorithm compared with the conventional least squares （LS） criteria based gradient-type AJD algorithms. The algorithm is attractive for practical applications since it is simple and efficient.
基金supported by the Important National Science & Technology Specific Projects(2010ZX03005-001-0)the Hi-Tech Research and Development of China(2006AA01Z272)the New Century Excellent Talents in University(NCET):(NCET-11-0593)
文摘In multi-cell cooperative multi-input multi-output （MIMO） systems, base station （BS） can exchange and utilize channel state information （CSI） of adjacent cell users to manage co-channel interference. Users quantize the CSIs of desired channel and interference channels using finite-rate feedback links, then BS can generate cooperative block diagonalization （BD） precoding matrices using the obtained quantized CSI at transmitter to supress co-channel interference. In this paper, a novel adaptive bit allocation scheme is proposed to minimize the rate loss due to imperfect CSI. We derive the closed-form expression of rate loss caused by both channel delay and limited feedback. Based on the derived rate loss expression, the proposed scheme can adaptively allocate more bits to quantize the better channels with smaller delays and fewer bits to worse channels with larger delays. Simulation results show that the proposed scheme yields higher performance than other allocation schemes.
基金supported by the National Program on Key Research Projects(Grant No.MOST2022YFA1402700)the National Natural Science Foundation of China(Grant Nos.12304176,12274187,12247183,and 12247101)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220876)partially supported by the High-Performance Computing Platform of Nanjing University of Aeronautics and Astronautics。
文摘Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges,which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects.This,in turn,generates many intriguing field-induced novel phases and the thermal Hall effect.In this review,we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′exchange from a numerical perspective.The review discusses certain representative exotic phases such as𝛤spin liquid,nematic ferromagnet,spin-flop phase,and distinct chiral spin states with spontaneous time-reversal symmetry breaking.It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.
基金supported by the Key Project from Education Department of Anhui Province (No.KJ2013A076)the PhD Programs Foundation of Ministry of Education of China (No.20120072110040)+1 种基金the National Natural Science Foundation of China (Nos.61133010,31071168,and 61005010)the China Postdoctoral Science Foundation (No.2012T50582)
文摘Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numerical characterizations and similarity analysis of sequences. Initially, a transformation method was introduced to represent each DNA sequence with dinucleotide physicochemical property matrix. Then, based on the approximate joint diagonalization theory, an eigenvalue vector was extracted from each DNA sequence,which could be considered as descriptor of the DNA sequence. Moreover, similarity analyses were performed by calculating the pair-wise distances among the obtained eigenvalue vectors. The results show that the proposed approach can capture more sequence information, and can jointly analyze the information contained in all involved multiple sequences, rather than separately, whose effectiveness was demonstrated intuitively by constructing a dendrogram for the 15 beta-globin gene sequences.
