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.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

The Limit Distribution of Stochastic Evolution Equations Driven by-Stable Non-Gaussian Noise

We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.

Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.

An improved predictive deconvolution based on maximization of non-Gaussianity

The predictive deconvolution algorithm （PD）, which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data （primaries and multiples） have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm （IPD） by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.

ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LVY NOISES

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.

Alternative non-Gaussianity measures for quantum states based on quantum fidelity

We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [Phys. Lett. A 373 58(2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert–Schmidt metric and the relative entropy metric. We make a comparative study between all existing nonGaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.

Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert–Schmidt distance

Non-Gaussianity of quantum states is a very important source for quantum information technology and can be quantified by using the known squared Hilbert–Schmidt distance recently introduced by Genoni et al.(Phys. Rev. A 78 042327(2007)). It is, however, shown that such a measure has many imperfects such as the lack of the swapping symmetry and the ineffectiveness evaluation of even Schr?dinger-cat-like states with small amplitudes. To deal with these difficulties, we propose an improved measure of non-Gaussianity for quantum states and discuss its properties in detail. We then exploit this improved measure to evaluate the non-Gaussianities of some relevant single-mode non-Gaussian states and multi-mode non-Gaussian entangled states. These results show that our measure is reliable. We also introduce a modified measure for Gaussianity following Mandilara and Cerf(Phys. Rev. A 86 030102(R)(2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.

Generation of Non-Gaussian Random Vibration Excitation Signal for Reliability Enhancement Test

During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal

Theory of Quantum Dissipation in a Class of Non-Gaussian Environments

In this work we construct a novel dissipaton-equation-of-motion （DEOM） theory in quadratic bath coupling environment, based on an extended algebraic statistical quasi-particle approach. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation via a totally different approach. We prove that the new theory, if it starts with the identical setup, constitutes the dynamical resolutions to the extended Zusman equation. Thus, we verify the generalized （non-Gaussian） Wick＇s theorem with dissipatons-pair added. This new algebraic ingredient enables the dissipaton approach being naturally extended to nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling case, the influence of a non-Gaussian environment cannot be completely characterized with the linear response theory. The new theory has to take this fact into account. The developed DEOM theory manifests the dynamical interplay between dissipatons and nonlinear bath coupling descriptors that will be specified. Numerical demonstrations will be given with the optical line shapes in quadratic coupling environment.

Robust detector for range-spread targets in non-Gaussian background

Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for sparse scatterer density, the detection of target scatterer in each range cell is derived, and then an M/K detector is proposed to detect the whole range-spread target. Se- condly, an integrating detector is devised to detect a range-spread target with dense scatterer density. Finally, to make the best of the advantages of M/K detector and integrating detector, a robust detector based on scatterer density （DBSD） is designed, which can reduce the probable collapsing loss or quantization error ef- fectively. Moreover, the density decision factor of DBSD is also determined. The formula of the false alarm probability is derived for DBSD. It is proved that the DBSD ensures a constant false alarm rate property. Furthermore, the computational results indi- cate that the DBSD is robust to different clutter one-lag correlations and target scatterer densities. It is also shown that the DBSD out- performs the existing scatterer-density-dependent detector.

Space-time clutter model for airborne bistatic radar with non-Gaussian statistics

To validate the potential space-time adaptive processing （STAP） algorithms for airborne bistatic radar clutter suppression under nonstationary and non-Gaussian clutter environments, a statistically non-Gaussian, space-time clutter model in varying bistatic geometrical scenarios is presented. The inclusive effects of the model contain the range dependency of bistatic clutter spectrum and clutter power variation in range-angle cells. To capture them, a new approach to coordinate system conversion is initiated into formulating bistatic geometrical model, and the bistatic non-Gaussian amplitude clutter representation method based on a compound model is introduced. The veracity of the geometrical model is validated by using the bistatic configuration parameters of multi-channel airborne radar measurement （MCARM） experiment. And simulation results manifest that the proposed model can accurately shape the space-time clutter spectrum tied up with specific airborne bistatic radar scenario and can characterize the heterogeneity of clutter amplitude distribution in practical clutter environments.

Stochastic properties of tumor growth with coupling between non-Gaussian and Gaussian noise terms

Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect.

Statistic PID Tracking Control for Non-Gaussian Stochastic Systems Based on T-S Fuzzy Model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Online Predictive Monitoring and Prediction Model for a Periodic Process Through Multiway Non-Gaussian Modeling

A new on-line predictive monitoring and prediction model for periodic biological processes is proposed using the multiway non-Gaussian modeling. The basic idea of this approach is to use multiway non-Gaussian modeling to extract some dominant key components from daily normal operation data in a periodic process, and subsequently combining these components with predictive statistical process monitoring techniques. The proposed predictive monitoring method has been applied to fault detection and diagnosis in the biological wastewater-treatment process, which is based on strong diurnal characteristics. The results show the power and advantages of the proposed predictive monitoring of a continuous process using the multiway predictive monitoring concept, which is thus able to give very useful conceptual results for a daily monitoring process and also enables a more rapid detection of the process fault than other traditional monitoring methods.

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.

Probabilistic Analysis and Fatigue Damage Assessment of Offshore Mooring System due to Non-Gaussian Bimodal Tension Processes

Both wave-frequency(WF) and low-frequency(LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system.This paper conducts a comprehensive investigation of applicable probability density functions(PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method.Short-term statistical characteristics of mooring-line tension responses are firstly investigated,in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients.Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes.Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components.A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses.Using time domain simulation as a benchmark,its accuracy is further validated using a numerical case study of a moored semi-submersible platform.

Variational Quality Control of Non-Gaussian Innovations in the GRAPES m3DVAR System: Mass Field Evaluation of Assimilation Experiments

The existence of outliers can seriously influence the analysis of variational data assimilation.Quality control allows us to effectively eliminate or absorb these outliers to produce better analysis fields.In particular,variational quality control(VarQC) can process gray zone outliers and is thus broadly used in variational data assimilation systems.In this study,governing equations are derived for two VarQC algorithms that utilize different contaminated Gaussian distributions(CGDs): Gaussian plus flat distribution and Huber norm distribution.As such,these VarQC algorithms can handle outliers that have non-Gaussian innovations.Then,these VarQC algorithms are implemented in the Global/Regional Assimilation and PrEdiction System(GRAPES) model-level three-dimensional variational data assimilation(m3 DVAR) system.Tests using artificial observations indicate that the VarQC method using the Huber distribution has stronger robustness for including outliers to improve posterior analysis than the VarQC method using the Gaussian plus flat distribution.Furthermore,real observation experiments show that the distribution of observation analysis weights conform well with theory,indicating that the application of VarQC is effective in the GRAPES m3 DVAR system.Subsequent case study and longperiod data assimilation experiments show that the spatial distribution and amplitude of the observation analysis weights are related to the analysis increments of the mass field(geopotential height and temperature).Compared to the control experiment,VarQC experiments have noticeably better posterior mass fields.Finally,the VarQC method using the Huber distribution is superior to the VarQC method using the Gaussian plus flat distribution,especially at the middle and lower levels.

Anomalous scaling in a non-Gaussian random shell model for passive scalars

In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.

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.