Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system.

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.

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.

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.

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.

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

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.

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.

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.

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.

基于Gaussian、ECOSAR模型的紫外/次氯酸体系降解含卤阻燃剂的产物预测与毒性评估

含卤阻燃剂广泛应用于各类电子产品的生产,难降解且具有生物毒性.在生产和使用过程中,部分含卤阻燃剂会残留在水体并排放到水环境造成累积污染,威胁水环境安全,亟需探寻有效的降解去毒方法.本研究通过Gaussian与ECOSAR模型预测了四氯双酚A(TCBPA)、四溴双酚A(TBBPA)、十溴二苯乙烷(DBDPE)等3种典型含卤阻燃剂在紫外/次氯酸(UV/Cl)体系中的光催氧化降解路径与产物毒性.结果表明,UV/Cl体系中的含氯自由基(RCS)与羟基自由基(·OH)易攻击阻燃剂分子结构上键能较低、Fukui指数较高的位点,促使C—Cl键、C—Br键、C—C键等因为受到攻击而断裂,进而降解阻燃剂.同时,利用ECOSAR模型评估发现降解产物的急性毒性LC_(50)-96 h均低于100 mg·L^(-1),佐证了UV/Cl体系对含卤阻燃剂降解的有效性,并降低其环境危害.因此,采用Gaussian计算、ECOSAR模型相结合的分析方法,能够更加便捷地预测阻燃剂降解路径与产物毒性特征,为深入揭示UV/Cl体系光催氧化降解含卤阻燃剂机理提供新思路.

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.

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises:Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.

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.

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.

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.

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.

Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer

Wind field simulation in the surface layer is often used to manage natural resources in terms of air quality,gene flow(through pollen drift),and plant disease transmission(spore dispersion).Although Lagrangian stochastic(LS)models describe stochastic wind behaviors,such models assume that wind velocities follow Gaussian distributions.However,measured surface-layer wind velocities show a strong skewness and kurtosis.This paper presents an improved model,a non-Gaussian LS model,which incorporates controllable non-Gaussian random variables to simulate the targeted non-Gaussian velocity distribution with more accurate skewness and kurtosis.Wind velocity statistics generated by the non-Gaussian model are evaluated by using the field data from the Cooperative Atmospheric Surface Exchange Study,October 1999 experimental dataset and comparing the data with statistics from the original Gaussian model.Results show that the non-Gaussian model improves the wind trajectory simulation by stably producing precise skewness and kurtosis in simulated wind velocities without sacrificing other features of the traditional Gaussian LS model,such as the accuracy in the mean and variance of simulated velocities.This improvement also leads to better accuracy in friction velocity(i.e.,a coupling of three-dimensional velocities).The model can also accommodate various non-Gaussian wind fields and a wide range of skewness–kurtosis combinations.Moreover,improved skewness and kurtosis in the simulated velocity will result in a significantly different dispersion for wind/particle simulations.Thus,the non-Gaussian model is worth applying to wind field simulation in the surface layer.

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.