Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function.As an application,we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states:a mixture of vacuum and Fock states,single-photon added thermal states,and even/odd Schr¨odinger cat states.It is shown that such a criterion is faithful and effective for revealing non-Gaussianity.We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Multi-Source Underwater DOA Estimation Using PSO-BP Neural Network Based on High-Order Cumulant Optimization

Due to the complex and changeable environment under water,the performance of traditional DOA estimation algorithms based on mathematical model,such as MUSIC,ESPRIT,etc.,degrades greatly or even some mistakes can be made because of the mismatch between algorithm model and actual environment model.In addition,the neural network has the ability of generalization and mapping,it can consider the noise,transmission channel inconsistency and other factors of the objective environment.Therefore,this paper utilizes Back Propagation(BP)neural network as the basic framework of underwater DOA estimation.Furthermore,in order to improve the performance of DOA estimation of BP neural network,the following three improvements are proposed.(1)Aiming at the problem that the weight and threshold of traditional BP neural network converge slowly and easily fall into the local optimal value in the iterative process,PSO-BP-NN based on optimized particle swarm optimization(PSO)algorithm is proposed.(2)The Higher-order cumulant of the received signal is utilized to establish the training model.(3)A BP neural network training method for arbitrary number of sources is proposed.Finally,the effectiveness of the proposed algorithm is proved by comparing with the state-of-the-art algorithms and MUSIC algorithm.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Spatiotemporal changes of gross primary productivity and its response to drought in the Mongolian Plateau under climate change

Gross primary productivity(GPP)of vegetation is an important constituent of the terrestrial carbon sinks and is significantly influenced by drought.Understanding the impact of droughts on different types of vegetation GPP provides insight into the spatiotemporal variation of terrestrial carbon sinks,aiding efforts to mitigate the detrimental effects of climate change.In this study,we utilized the precipitation and temperature data from the Climatic Research Unit,the standardized precipitation evapotranspiration index(SPEI),the standardized precipitation index(SPI),and the simulated vegetation GPP using the eddy covariance-light use efficiency(EC-LUE)model to analyze the spatiotemporal change of GPP and its response to different drought indices in the Mongolian Plateau during 1982-2018.The main findings indicated that vegetation GPP decreased in 50.53% of the plateau,mainly in its northern and northeastern parts,while it increased in the remaining 49.47%area.Specifically,meadow steppe(78.92%)and deciduous forest(79.46%)witnessed a significant decrease in vegetation GPP,while alpine steppe(75.08%),cropland(76.27%),and sandy vegetation(87.88%)recovered well.Warming aridification areas accounted for 71.39% of the affected areas,while 28.53% of the areas underwent severe aridification,mainly located in the south and central regions.Notably,the warming aridification areas of desert steppe(92.68%)and sandy vegetation(90.24%)were significant.Climate warming was found to amplify the sensitivity of coniferous forest,deciduous forest,meadow steppe,and alpine steppe GPP to drought.Additionally,the drought sensitivity of vegetation GPP in the Mongolian Plateau gradually decreased as altitude increased.The cumulative effect of drought on vegetation GPP persisted for 3.00-8.00 months.The findings of this study will improve the understanding of how drought influences vegetation in arid and semi-arid areas.

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

Joint estimation of DOA, frequency, and polarization based on cumulants and UCA

A joint estimation algorithm of direction of arrival （DOA）, frequency, and polarization, based on fourth-order cumulants and uniform circular array （UCA） of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.

CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES

The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.

Non-Gaussianity dynamics of two-mode squeezed number states subject to different types of noise based on cumulant theory

We provide a measure to characterize the non-Gaussianity of phase-space function of bosonic quantum states based on the cumulant theory. We study the non-Gaussianity dynamics of two-mode squeezed number states by analyzing the phase-averaged kurtosis for two different models of decoherence： amplitude damping model and phase damping model.For the amplitude damping model, the non-Gaussianity is very fragile and completely vanishes at a finite time. For the phase damping model, such states exhibit rich non-Gaussian characters. In particular, we obtain a transition time that such states can transform from sub-Gaussianity into super-Gaussianity during the evolution. Finally, we compare our measure with the existing measures of non-Gaussianity under the independent dephasing environment.

Application of Three Order Cumulants in Fault Diagnosis

The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.

Recognition Analysis and Simulation Implementation Based on High-Order Cumulants of Wireless Digital Modulation Mode

This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.

A Cumulant-Based Beamforming Algorithm for CDMA Frequency-nonselective Fading Channel

A cumulant-based beamforing technique for synchronous CDMA system with decorrelator is presented. With decorrelating detector the proposed algorithm has the advantages that the steering vector of desired user’s can be estimated independently by eliminating all the other resolved signal interferences. Furthermore employing cumulant-based signal processing technique the steering vector of the decoupled signals can be estimated blindly. Simulation results show that the cumulant-based beamformer demonstrates excellent performance.

ADAPTIVE ALGORITHM FOR CONSISTENTMA PARAMETER ESTIMATION VIATHIRD ORDER CUMULANT

This paper addresses the problem of adaptive,consistent parameter estimation for a MA model from the 3rd order cumulant of the system output. The proposed adaptive algorithm is derived by using the new linear equation system (J. K. Tugnait, 1990), which is proved to have unique solution,and hence guarantees the consistence of the MA parameters. Simulation results are provided to show the performance of the new algorithm.

A MODIFIED HIGH-ORDER CUMULANT MUSIC ALGORITHM FOR SIGNAL DOA ESTIMATION

This paper gives a MUSIC signal DOA estimation algorithm based on the modified high-order cumulant matrix which is constructed by the recieved data and their conjugate rearrangements. When the snapshot number is limited, this algorithm can improve the signal DOA estimation performances obviously, and its computational complexity scarcely increases. Finally, some simulation results to verify the theoretical analyses are presented.

Harmonic Retrieval Embedded in Hybrid Colored Noise: a Novel Pisarenko Method Based on Cross high order Cumulant

Spectral estimation method is an effective method in the case of parameter estimation of sinusoid signal in noises.It always applies cross spectral estimation theory and high order self spectral estimation methods up to now.Yule Walker equation based on cross fourth order cumulant is developed and Pisarenko method is provided in this paper.Simulation results show that the method is effective to retrieve sinusoid signal frequencies from hybrid colored noises and has good performance.

Photon number cumulant expansion and generating function for photon added-and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.

ANALYSIS OF A CUMULANT-BASED 2D-RAKE RECEIVER FOR CDMA SYSTEM OVER FREQUENCY-SELECTIVE FADING CHANNELS

The conventional 2D Rake receivers for code division multiple access (CDMA) system over frequency selective fading channels are generally based on the second order statistics while assuming perfect array conditions. However, the sensor response, location uncertainty, and the use of sample statistics can severely degrade the performance of second order statistics processing. And in practical application, it is impossible to calibrate the array frequently. In this paper a cumulant based 2D Rake receiver for synchronous CDMA system with decorrelator is presented. Decorrelating is a multi user detection approach that not only provides a fundamental solution to the mutual interference problem in CDMA communications but also makes it convenient for the decoupled signal to be processed spatially and temporally. High order signal processing has some inherent advantages over that of second order. Employing second order statistics it is impossible to estimate source steering vector blindly, while employing higher than second order cumulants, this purpose can be achieved. The performance analysis shows that employing cumulant based signal processing technique the proposed 2D Rake receiver is blind and demonstrates excellent performance.

THE FOURTH-ORDER CUMULANTS BASED SPECTRALESTIMATION METHOD AND ITS APPLICATIONTO DIRECTION-FINDING

Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.