Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability th...Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability theory(FPT).Using big data collected from phasor measurement units(PMUs),we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states.The event detection matrix is further described as an information matrix plus a noise matrix,and the essence of event detection is to extract event information from the event detection matrix.By associating the event detection problem with FPT,the empirical spectral distributions(ESDs)related moments of the sample covariance matrix of the information matrix are computed,to distinguish events from“noises”,including normal fluctuations,background noises,and measurement errors.Based on central limit theory(CLT),the alarm threshold is computed using measurements collected in normal states.Additionally,with the aid of sliding window,this paper builds an event detection architecture to reflect power grid state and detect events online.Case studies with simulated data from Anhui,China,and real PMU data from Guangdong,China,verify the effectiveness of the proposed method.Compared with other data-driven methods,the proposed method is more sensitive and has better adaptability to the normal fluctuations,background noises,and measurement errors in real PMU cases.In addition,it does not require large number of training samples as needed in the training-testing paradigm.展开更多
Inspired by Speicher's multidimensional free central limit theorem and semicircle families, we prove an in?nite dimensional compound Poisson limit theorem in free probability, and de?ne in?nite dimensional compoun...Inspired by Speicher's multidimensional free central limit theorem and semicircle families, we prove an in?nite dimensional compound Poisson limit theorem in free probability, and de?ne in?nite dimensional compound free Poisson distributions in a non-commutative probability space. In?nite dimensional free in?nitely divisible distributions are de?ned and characterized in terms of their free cumulants. It is proved that for a sequence of random variables, the following three statements are equivalent:(1) the distribution of the sequence is multidimensional free in?nitely divisible;(2) the sequence is the limit in distribution of a sequence of triangular trays of families of random variables;(3) the sequence has the same distribution as that of {a_1^((i)): i = 1, 2,...}of a multidimensional free L′evy process {{a_1^((i)): i = 1, 2,...} : t≥0}. Under certain technical assumptions, this is the case if and only if the sequence is the limit in distribution of a sequence of sequences of random variables having multidimensional compound free Poisson distributions.展开更多
High-throughput satellites(HTSs) play an important role in future millimeter-wave(mm Wave) aeronautical communication to meet high speed and broad bandwidth requirements. This paper investigates the outage performance...High-throughput satellites(HTSs) play an important role in future millimeter-wave(mm Wave) aeronautical communication to meet high speed and broad bandwidth requirements. This paper investigates the outage performance of an aeronautical broadband satellite communication system’s forward link, where the feeder link from the gateway to the HTS uses free-space optical(FSO) transmission and the user link from the HTS to aircraft operates at the mm Wave band. In the user link, spot beam technology is exploited at the HTS and a massive antenna array is deployed at the aircraft. We first present a location-based beamforming(BF) scheme to maximize the expected output signal-to-noise ratio(SNR) of the forward link with the amplify-and-forward(AF) protocol,which turns out to be a phased array. Then, by supposing that the FSO feeder link follows Gamma-Gamma fading whereas the mm Wave user link experiences shadowed Rician fading, we take the influence of the phase error into account, and derive the closed-form expression of the outage probability(OP) for the considered system. To gain further insight, a simple asymptotic OP expression at a high SNR is provided to show the diversity order and coding gain. Finally, numerical simulations are conducted to confirm the validity of the theoretical analysis and reveal the effects of phase errors on the system outage performance.展开更多
A robust method is proposed for estimating discrete probability functions for small samples. The proposed approach introduces and minimizes a parameterized objective function that is analogous to free energy functions...A robust method is proposed for estimating discrete probability functions for small samples. The proposed approach introduces and minimizes a parameterized objective function that is analogous to free energy functions in statistical physics. A key feature of the method is a model of the parameter that controls the trade-off between likelihood and robustness in response to the degree of fluctuation. The method thus does not require the value of the parameter to be manually selected. It is proved that the estimator approaches the maximum likelihood estimator at the asymptotic limit. The effectiveness of the method in terms of robustness is demonstrated by experimental studies on point estimation for probability distributions with various entropies.展开更多
Communication networks have undergone rapid developments in the past few decades in many Sub-Saharan African countries. The increasing number of subscribers and demand for greater variety of services in these countrie...Communication networks have undergone rapid developments in the past few decades in many Sub-Saharan African countries. The increasing number of subscribers and demand for greater variety of services in these countries make it difficult for network operators to provide the service varieties subscribers want while maintaining acceptable levels of quality of service. This paper analyzes the radio network of cellular networks in terms of traffic distribution over the existing number of communication channels using MATLAB/Simulink. A scale-free user network, which takes into account user behavior in a realistic physical network, has been used to model a more realistic cause for call blockings in a typical cellular network deployment under a Sub-Saharan environment. Peak recorded traffic distribution was observed to have overwhelmed the existing number of channels provided by the network operators for some cells eventually leading to increase in call drop rates. This high call blocking probability was attributed to poor network monitoring by the network operators to match the ever changing traffic intensities.展开更多
We give two applications of logarithmic Sobolev inequalities to matrix models and free probability. We also provide a new characterization of semi-circular systems through a Poincaré-type inequality.
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
The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 ...The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.展开更多
Ambient backscatter is a new green technology for Internet of Things(IoT)that utilizes surrounding wireless signals to enable batteryless devices to communicate with other devices.The battery-free devices first harves...Ambient backscatter is a new green technology for Internet of Things(IoT)that utilizes surrounding wireless signals to enable batteryless devices to communicate with other devices.The battery-free devices first harvest energy from ambient wireless signals and then backscatter the signals for communications.Clearly,sensitivity and distance are two important parameters for system performance.However,most existing studies on ambient backscatter communication systems do not consider the impact of the sensitivity of the energy-harvesting nodes and the distances between these devices.In this paper,we first provide a literature review for ambient communication technology and then take sensitivity and distance as two key parameters and investigate the sensitivity and distance based performance for ambient backscatter communication systems.Specifically,we establish the mathematical model based on distances between transceivers and backscattering nodes,extract a parameter that can differentiate the direct path and the backscattering path,evaluate the effects of transmit beamforming,design an energy detector for the reader,and analyze the outage probability of energy harvesting at the tag and the bit error rate(BER)at the reader.Simulations are then provided to corroborate the proposed studies.展开更多
Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the pha...Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.展开更多
基金supported by the National Key Research and Development Program of China(No.2021YFB2401302)。
文摘Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability theory(FPT).Using big data collected from phasor measurement units(PMUs),we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states.The event detection matrix is further described as an information matrix plus a noise matrix,and the essence of event detection is to extract event information from the event detection matrix.By associating the event detection problem with FPT,the empirical spectral distributions(ESDs)related moments of the sample covariance matrix of the information matrix are computed,to distinguish events from“noises”,including normal fluctuations,background noises,and measurement errors.Based on central limit theory(CLT),the alarm threshold is computed using measurements collected in normal states.Additionally,with the aid of sliding window,this paper builds an event detection architecture to reflect power grid state and detect events online.Case studies with simulated data from Anhui,China,and real PMU data from Guangdong,China,verify the effectiveness of the proposed method.Compared with other data-driven methods,the proposed method is more sensitive and has better adaptability to the normal fluctuations,background noises,and measurement errors in real PMU cases.In addition,it does not require large number of training samples as needed in the training-testing paradigm.
基金supported by National Natural Science Foundation of China (Grant Nos. 11101220, 11271199 and 11671214)Visiting Scholar Project Funded (Grant No. 96172373)the Fundamental Research Funds for the Central Universities
文摘Inspired by Speicher's multidimensional free central limit theorem and semicircle families, we prove an in?nite dimensional compound Poisson limit theorem in free probability, and de?ne in?nite dimensional compound free Poisson distributions in a non-commutative probability space. In?nite dimensional free in?nitely divisible distributions are de?ned and characterized in terms of their free cumulants. It is proved that for a sequence of random variables, the following three statements are equivalent:(1) the distribution of the sequence is multidimensional free in?nitely divisible;(2) the sequence is the limit in distribution of a sequence of triangular trays of families of random variables;(3) the sequence has the same distribution as that of {a_1^((i)): i = 1, 2,...}of a multidimensional free L′evy process {{a_1^((i)): i = 1, 2,...} : t≥0}. Under certain technical assumptions, this is the case if and only if the sequence is the limit in distribution of a sequence of sequences of random variables having multidimensional compound free Poisson distributions.
基金Project supported by the Key International Cooperation Research Project (No. 61720106003)the National Natural Science Foundation of China (No. 61801234)+2 种基金the Shanghai Aerospace Science and Technology Innovation Foundation (No. SAST2019-095)the Research Project of Science and Technology on Complex Electronic System Simulation Laboratory (No. DXZT-JCZZ-2019-009),NUPTSF (No. NY220111)the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China (Nos. KYCX190950 and KYCX200724)。
文摘High-throughput satellites(HTSs) play an important role in future millimeter-wave(mm Wave) aeronautical communication to meet high speed and broad bandwidth requirements. This paper investigates the outage performance of an aeronautical broadband satellite communication system’s forward link, where the feeder link from the gateway to the HTS uses free-space optical(FSO) transmission and the user link from the HTS to aircraft operates at the mm Wave band. In the user link, spot beam technology is exploited at the HTS and a massive antenna array is deployed at the aircraft. We first present a location-based beamforming(BF) scheme to maximize the expected output signal-to-noise ratio(SNR) of the forward link with the amplify-and-forward(AF) protocol,which turns out to be a phased array. Then, by supposing that the FSO feeder link follows Gamma-Gamma fading whereas the mm Wave user link experiences shadowed Rician fading, we take the influence of the phase error into account, and derive the closed-form expression of the outage probability(OP) for the considered system. To gain further insight, a simple asymptotic OP expression at a high SNR is provided to show the diversity order and coding gain. Finally, numerical simulations are conducted to confirm the validity of the theoretical analysis and reveal the effects of phase errors on the system outage performance.
文摘A robust method is proposed for estimating discrete probability functions for small samples. The proposed approach introduces and minimizes a parameterized objective function that is analogous to free energy functions in statistical physics. A key feature of the method is a model of the parameter that controls the trade-off between likelihood and robustness in response to the degree of fluctuation. The method thus does not require the value of the parameter to be manually selected. It is proved that the estimator approaches the maximum likelihood estimator at the asymptotic limit. The effectiveness of the method in terms of robustness is demonstrated by experimental studies on point estimation for probability distributions with various entropies.
文摘Communication networks have undergone rapid developments in the past few decades in many Sub-Saharan African countries. The increasing number of subscribers and demand for greater variety of services in these countries make it difficult for network operators to provide the service varieties subscribers want while maintaining acceptable levels of quality of service. This paper analyzes the radio network of cellular networks in terms of traffic distribution over the existing number of communication channels using MATLAB/Simulink. A scale-free user network, which takes into account user behavior in a realistic physical network, has been used to model a more realistic cause for call blockings in a typical cellular network deployment under a Sub-Saharan environment. Peak recorded traffic distribution was observed to have overwhelmed the existing number of channels provided by the network operators for some cells eventually leading to increase in call drop rates. This high call blocking probability was attributed to poor network monitoring by the network operators to match the ever changing traffic intensities.
文摘We give two applications of logarithmic Sobolev inequalities to matrix models and free probability. We also provide a new characterization of semi-circular systems through a Poincaré-type inequality.
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Project Nos.10571065 and 10401011 supported by NSFC
文摘The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case （q=1） and fermionic case （q=-1）.In particular, when q=0 it＇s also compatible with the free case.
基金supported by Scientific Research Program of Beijing Municipal Commission of Education(No.KM201910853003)National key research and development program(2020YFB1806604)Fundamental Research Funds for the Central Universities(No.2020YJS044).
文摘Ambient backscatter is a new green technology for Internet of Things(IoT)that utilizes surrounding wireless signals to enable batteryless devices to communicate with other devices.The battery-free devices first harvest energy from ambient wireless signals and then backscatter the signals for communications.Clearly,sensitivity and distance are two important parameters for system performance.However,most existing studies on ambient backscatter communication systems do not consider the impact of the sensitivity of the energy-harvesting nodes and the distances between these devices.In this paper,we first provide a literature review for ambient communication technology and then take sensitivity and distance as two key parameters and investigate the sensitivity and distance based performance for ambient backscatter communication systems.Specifically,we establish the mathematical model based on distances between transceivers and backscattering nodes,extract a parameter that can differentiate the direct path and the backscattering path,evaluate the effects of transmit beamforming,design an energy detector for the reader,and analyze the outage probability of energy harvesting at the tag and the bit error rate(BER)at the reader.Simulations are then provided to corroborate the proposed studies.
基金Supported by the National Natural Science Foundation of China(11705106,11475107,12075143)the Natural Science Foundation of Shanxi Province,China(201901D111315)+2 种基金the Natural Science Foundation for Young Scientists of Shanxi Province,China(201901D211441)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472,2016173)the Science Technology Plan Project of Datong City,China(2020153)。
文摘Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.
