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
We have applied the Random Matrix Theory in order to examine the validity of the NPT treatment in HSP. We have investigated the pathology examining the sEMG recorded signal for about eight minutes. We have performed s...We have applied the Random Matrix Theory in order to examine the validity of the NPT treatment in HSP. We have investigated the pathology examining the sEMG recorded signal for about eight minutes. We have performed standard electromyographic investigations as well as we have applied the RMT method of analysis. We have investigated the sEMG signals before and after the NPT treatment. The application of a so robust method as the RMT evidences that the NPT treatment was able to induce a net improvement of the disease respect to the pathological status before NPT.展开更多
The impact of large-scale wind farms on power system stability should be carefully investigated,in which mal-functions usually exist in the collector line's relay protection.In order to solve this challenging prob...The impact of large-scale wind farms on power system stability should be carefully investigated,in which mal-functions usually exist in the collector line's relay protection.In order to solve this challenging problem,a novel time-domain protection scheme for collector lines,based on random matrix theory(RMT),is proposed in this paper.First,the collected currents are preprocessed to form time series data.Then,a real-time sliding time window is used to form a consecutive time series data matrix.Based on RMT,mean spectral radius(MSR)is used to analyze time series data characteristics after real-time calculations are performed.Case studies demonstrate that RMT is independent from fault locations and fault types.In particular,faulty and non-faulty collector lines can be accurately and efficiently identified compared with traditional protection schemes.展开更多
Faced with the tight coupling of multi energy sources,the interaction between different energy supply systems makes it difficult for integrated energy systems(IES)to identify weak nodes.Based on the analysis of the da...Faced with the tight coupling of multi energy sources,the interaction between different energy supply systems makes it difficult for integrated energy systems(IES)to identify weak nodes.Based on the analysis of the data generated by the actual operation of IES,this paper proposes a weak node identification method based on random matrix theory(RMT).First,establish a unified power flow model for IES.Secondly.introduce RMT and the characteristics of weak nodes,without considering the detailed physical model of the system,using historical data and real-time data to construct the random matrix.Thirdly,the two limit spectrum distribution functions(Marchenko-Pastur law and ring law)are used to qualitatively analyze the system’s operating status,calculate linear eigenvalue statistics such as mean spectral radius(MSR),and establish the weak node identification model based on entropy theory.Finally,the simulation of IES verifies the effectiveness of the proposed method and provides a new approach for the identification of weak nodes in IES.展开更多
The weighting subspace fitting(WSF)algorithm performs better than the multi-signal classification(MUSIC)algorithm in the case of low signal-to-noise ratio(SNR)and when signals are correlated.In this study,we use the r...The weighting subspace fitting(WSF)algorithm performs better than the multi-signal classification(MUSIC)algorithm in the case of low signal-to-noise ratio(SNR)and when signals are correlated.In this study,we use the random matrix theory(RMT)to improve WSF.RMT focuses on the asymptotic behavior of eigenvalues and eigenvectors of random matrices with dimensions of matrices increasing at the same rate.The approximative first-order perturbation is applied in WSF when calculating statistics of the eigenvectors of sample covariance.Using the asymptotic results of the norm of the projection from the sample covariance matrix signal subspace onto the real signal in the random matrix theory,the method of calculating WSF is obtained.Numerical results are shown to prove the superiority of RMT in scenarios with few snapshots and a low SNR.展开更多
Fault detection and location are critically significant applications of a supervisory control system in a smart grid.The methods,based on random matrix theory(RMT),have been practiced using measurements to detect shor...Fault detection and location are critically significant applications of a supervisory control system in a smart grid.The methods,based on random matrix theory(RMT),have been practiced using measurements to detect short circuit faults occurring on transmission lines.However,the diagnostic accuracy is infuenced by the noise signal in the measurements.The relationship between mean eigenvalue of a random matrix and noise is detected in this paper,and the defects of the Mean Spectral Radius(MSR),as an indicator to detect faults,are theoretically determined,along with a novel indicator of the shifting degree of maximum eigenvalue and its threshold.By comparing the indicator and the threshold,the occurrence of a fault can be assessed.Finally,an augmented matrix is constructed to locate the fault area.The proposed method can effectively achieve fault detection via the RMT without any influence of noise,and also does not depend on system models.The experiment results are based on the IEEE 39-bus system.Also,actual provincial grid data is applied to validate the effectiveness of the proposed method.展开更多
I discuss the results from a study of the central ^12CC collisions at 4.2 A GeV/c. The data have been analyzed using a new method based on the Random Matrix Theory. The simulation data coming from the Ultra Relativist...I discuss the results from a study of the central ^12CC collisions at 4.2 A GeV/c. The data have been analyzed using a new method based on the Random Matrix Theory. The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses. I found that the behavior of the nearest neighbor spacing distribution for the protons, neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data. I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.展开更多
Using the method based on Random Matrix Theory （RMT）, the results for the nearest-neighbor distributions obtained from the experimental data on ^12C-C collisions at 4.2 AGeV/c have been discussed and compared with t...Using the method based on Random Matrix Theory （RMT）, the results for the nearest-neighbor distributions obtained from the experimental data on ^12C-C collisions at 4.2 AGeV/c have been discussed and compared with the simulated data on ^12C-C collisions at 4.2 AGeV/c produced with the aid of the Dubna Cascade Model. The results show that the correlation of secondary particles decreases with an increasing number of charged particles Nch. These observed changes in the nearest-neighbor distributions of charged particles could be associated with the centrality variation of the collisions.展开更多
Construction of Global Energy Interconnection(GEI) is regarded as an effective way to utilize clean energy and it has been a hot research topic in recent years. As one of the enabling technologies for GEI, big data is...Construction of Global Energy Interconnection(GEI) is regarded as an effective way to utilize clean energy and it has been a hot research topic in recent years. As one of the enabling technologies for GEI, big data is accompanied with the sharing, fusion and comprehensive application of energy related data all over the world. The paper analyzes the technology innovation direction of GEI and the advantages of big data technologies in supporting GEI development, and then gives some typical application scenarios to illustrate the application value of big data. Finally, the architecture for applying random matrix theory in GEI is presented.展开更多
To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solut...To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.展开更多
In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer...In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer follows the generalized Marcenko-Pastur law,which is brand new.It is the first result on rank correlation matrices with dependence.As applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix.From these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.展开更多
A model is constructed to study the statistical properties of irregular trajectories of a log-gas whose positions are those of the complex eigenvalues of the unitary Ginibre ensemble. It is shown that statistically th...A model is constructed to study the statistical properties of irregular trajectories of a log-gas whose positions are those of the complex eigenvalues of the unitary Ginibre ensemble. It is shown that statistically the trajectories form a structure that reveals the eigenvalue departure positions. It is also shown that the curvatures of the ensemble of trajectories are Cauchy distributed.展开更多
Resilient power systems urgently need real-time evaluation of their operational states.By mining the characteristics of the grid operational data and mapping them to the operational state,this paper proposes a method ...Resilient power systems urgently need real-time evaluation of their operational states.By mining the characteristics of the grid operational data and mapping them to the operational state,this paper proposes a method to evaluate the real-time state and the evolution direction of power systems.First,the state evaluation matrix is constructed using nodal voltages.Then,from the data-driven perspective,the grid state is embodied in the operational data change.Furthermore,four indicators are proposed to characterize the power grid statefrom inherent physical and operating characteristics perspectives.Finally,through the simulations of a real power grid in China,it is shown that the method proposed in this paper can adequately characterize the power grid state,and is robust against bad data.展开更多
Cross-correlating traffic flow data at different intersections in an urban transportation network is important for understanding the collective behavior of constituents in a complex system and for predicting the risk ...Cross-correlating traffic flow data at different intersections in an urban transportation network is important for understanding the collective behavior of constituents in a complex system and for predicting the risk of network-wide congestion. In this work, a Random Matrix Theory （RMT） based method is used to describe the collective behavior from massive traffic data sets. Nonrandom correlations between traffic flow series recorded in the Beijing road network occur both with and without detrending. The effect of the traffic load on the correlation patterns of network-wide traffic flows is analyzed using the RMT analysis of a simulated data set collected from Paramics. The RMT analysis is also used to evaluate the impact of incidents on the network-wide traffic status. Cluster analysis is used to find the largest cluster in the network which indicates the critical congestion caused by the incident. All the results show that RMT analyses are an effective method for investigating systematic interactions in urban transportation systems.展开更多
The distributed antenna system （DAS） is considered as a promising architecture for future wireless access. This paper describes the uplink of a power-controlled circular-layout DAS （CL-DAS） with minimum mean-squar...The distributed antenna system （DAS） is considered as a promising architecture for future wireless access. This paper describes the uplink of a power-controlled circular-layout DAS （CL-DAS） with minimum mean-square error （MMSE） receivers. Results from random matrix theory are used to show that for such a DAS, the per-user sum rate and the total transmit power both converge as the number of users and antennas goes to infinity with a constant ratio of antennas to users. The relationship between the asymptotic per-user sum rate and the asymptotic total transmit power is given for all possible values of the radius of the circle on which antennas are placed. This rate-power relationship is then used to find the optimal radius. With this optimal radius, the CL-DAS is proved to offer a significant gain compared with a traditional co-located antenna system. Simulation results demonstrate the validity of the analysis and the superiority of the DAS.展开更多
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.
文摘We have applied the Random Matrix Theory in order to examine the validity of the NPT treatment in HSP. We have investigated the pathology examining the sEMG recorded signal for about eight minutes. We have performed standard electromyographic investigations as well as we have applied the RMT method of analysis. We have investigated the sEMG signals before and after the NPT treatment. The application of a so robust method as the RMT evidences that the NPT treatment was able to induce a net improvement of the disease respect to the pathological status before NPT.
基金the National Natural Science Foundation of China(No.51807085,52037003)Key Science and Technology Project of Yunnan Province,China(202002AF080001)。
文摘The impact of large-scale wind farms on power system stability should be carefully investigated,in which mal-functions usually exist in the collector line's relay protection.In order to solve this challenging problem,a novel time-domain protection scheme for collector lines,based on random matrix theory(RMT),is proposed in this paper.First,the collected currents are preprocessed to form time series data.Then,a real-time sliding time window is used to form a consecutive time series data matrix.Based on RMT,mean spectral radius(MSR)is used to analyze time series data characteristics after real-time calculations are performed.Case studies demonstrate that RMT is independent from fault locations and fault types.In particular,faulty and non-faulty collector lines can be accurately and efficiently identified compared with traditional protection schemes.
基金This work was supported in part by the National Key Research and Development Program of China(2018YFB0904200)Eponymous Complement S&T Program of State Grid Corporation of China(SGLNDKOOKJJS1800266).
文摘Faced with the tight coupling of multi energy sources,the interaction between different energy supply systems makes it difficult for integrated energy systems(IES)to identify weak nodes.Based on the analysis of the data generated by the actual operation of IES,this paper proposes a weak node identification method based on random matrix theory(RMT).First,establish a unified power flow model for IES.Secondly.introduce RMT and the characteristics of weak nodes,without considering the detailed physical model of the system,using historical data and real-time data to construct the random matrix.Thirdly,the two limit spectrum distribution functions(Marchenko-Pastur law and ring law)are used to qualitatively analyze the system’s operating status,calculate linear eigenvalue statistics such as mean spectral radius(MSR),and establish the weak node identification model based on entropy theory.Finally,the simulation of IES verifies the effectiveness of the proposed method and provides a new approach for the identification of weak nodes in IES.
基金Project supported by the National Natural Science Foundation of China(No.61976113)。
文摘The weighting subspace fitting(WSF)algorithm performs better than the multi-signal classification(MUSIC)algorithm in the case of low signal-to-noise ratio(SNR)and when signals are correlated.In this study,we use the random matrix theory(RMT)to improve WSF.RMT focuses on the asymptotic behavior of eigenvalues and eigenvectors of random matrices with dimensions of matrices increasing at the same rate.The approximative first-order perturbation is applied in WSF when calculating statistics of the eigenvectors of sample covariance.Using the asymptotic results of the norm of the projection from the sample covariance matrix signal subspace onto the real signal in the random matrix theory,the method of calculating WSF is obtained.Numerical results are shown to prove the superiority of RMT in scenarios with few snapshots and a low SNR.
基金This work was supported in part by the National Natural Science Foundation of China(Key Project Number:51437003)。
文摘Fault detection and location are critically significant applications of a supervisory control system in a smart grid.The methods,based on random matrix theory(RMT),have been practiced using measurements to detect short circuit faults occurring on transmission lines.However,the diagnostic accuracy is infuenced by the noise signal in the measurements.The relationship between mean eigenvalue of a random matrix and noise is detected in this paper,and the defects of the Mean Spectral Radius(MSR),as an indicator to detect faults,are theoretically determined,along with a novel indicator of the shifting degree of maximum eigenvalue and its threshold.By comparing the indicator and the threshold,the occurrence of a fault can be assessed.Finally,an augmented matrix is constructed to locate the fault area.The proposed method can effectively achieve fault detection via the RMT without any influence of noise,and also does not depend on system models.The experiment results are based on the IEEE 39-bus system.Also,actual provincial grid data is applied to validate the effectiveness of the proposed method.
文摘I discuss the results from a study of the central ^12CC collisions at 4.2 A GeV/c. The data have been analyzed using a new method based on the Random Matrix Theory. The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses. I found that the behavior of the nearest neighbor spacing distribution for the protons, neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data. I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.
文摘Using the method based on Random Matrix Theory （RMT）, the results for the nearest-neighbor distributions obtained from the experimental data on ^12C-C collisions at 4.2 AGeV/c have been discussed and compared with the simulated data on ^12C-C collisions at 4.2 AGeV/c produced with the aid of the Dubna Cascade Model. The results show that the correlation of secondary particles decreases with an increasing number of charged particles Nch. These observed changes in the nearest-neighbor distributions of charged particles could be associated with the centrality variation of the collisions.
基金supported by National High-technology Research and Development Program of China (863 Program) (2015AA050203)the State Grid Science and Technology Project (5442DZ170019-P)
文摘Construction of Global Energy Interconnection(GEI) is regarded as an effective way to utilize clean energy and it has been a hot research topic in recent years. As one of the enabling technologies for GEI, big data is accompanied with the sharing, fusion and comprehensive application of energy related data all over the world. The paper analyzes the technology innovation direction of GEI and the advantages of big data technologies in supporting GEI development, and then gives some typical application scenarios to illustrate the application value of big data. Finally, the architecture for applying random matrix theory in GEI is presented.
基金V. ACKN0WLEDGMENT This work was supported by the National Natural Sci- ence Foundation of China （No.10375024） and the Science Foundation of Hunan Educational Committee.
文摘To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.
基金supported by National Natural Science Foundation of China(Grant Nos.12031005 and 12101292)supported by National Natural Science Foundation of China(Grant No.12031005),supported by National Natural Science Foundation of China(Grant No.12171099)Natural Science Foundation of Shanghai(Grant No.21ZR1432900)。
文摘In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer follows the generalized Marcenko-Pastur law,which is brand new.It is the first result on rank correlation matrices with dependence.As applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix.From these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.
基金supported by the Brazilian agencies CNPq and FAPESP
文摘A model is constructed to study the statistical properties of irregular trajectories of a log-gas whose positions are those of the complex eigenvalues of the unitary Ginibre ensemble. It is shown that statistically the trajectories form a structure that reveals the eigenvalue departure positions. It is also shown that the curvatures of the ensemble of trajectories are Cauchy distributed.
基金supported by National Natural Science Foundation of China under Grant No.51907096.
文摘Resilient power systems urgently need real-time evaluation of their operational states.By mining the characteristics of the grid operational data and mapping them to the operational state,this paper proposes a method to evaluate the real-time state and the evolution direction of power systems.First,the state evaluation matrix is constructed using nodal voltages.Then,from the data-driven perspective,the grid state is embodied in the operational data change.Furthermore,four indicators are proposed to characterize the power grid statefrom inherent physical and operating characteristics perspectives.Finally,through the simulations of a real power grid in China,it is shown that the method proposed in this paper can adequately characterize the power grid state,and is robust against bad data.
基金Supported by the National Natural Science Foundation of China(Nos. 60721003 and 60834001)the National High-Tech Research and Development (863) Program of China (Nos. 2012AA112305,2011AA110301, and 2011AA110401)
文摘Cross-correlating traffic flow data at different intersections in an urban transportation network is important for understanding the collective behavior of constituents in a complex system and for predicting the risk of network-wide congestion. In this work, a Random Matrix Theory （RMT） based method is used to describe the collective behavior from massive traffic data sets. Nonrandom correlations between traffic flow series recorded in the Beijing road network occur both with and without detrending. The effect of the traffic load on the correlation patterns of network-wide traffic flows is analyzed using the RMT analysis of a simulated data set collected from Paramics. The RMT analysis is also used to evaluate the impact of incidents on the network-wide traffic status. Cluster analysis is used to find the largest cluster in the network which indicates the critical congestion caused by the incident. All the results show that RMT analyses are an effective method for investigating systematic interactions in urban transportation systems.
基金Supported by the National Natural Science Foundation of China (No. 90204001)
文摘The distributed antenna system （DAS） is considered as a promising architecture for future wireless access. This paper describes the uplink of a power-controlled circular-layout DAS （CL-DAS） with minimum mean-square error （MMSE） receivers. Results from random matrix theory are used to show that for such a DAS, the per-user sum rate and the total transmit power both converge as the number of users and antennas goes to infinity with a constant ratio of antennas to users. The relationship between the asymptotic per-user sum rate and the asymptotic total transmit power is given for all possible values of the radius of the circle on which antennas are placed. This rate-power relationship is then used to find the optimal radius. With this optimal radius, the CL-DAS is proved to offer a significant gain compared with a traditional co-located antenna system. Simulation results demonstrate the validity of the analysis and the superiority of the DAS.
