A recursive calculating algorithm for higher-order cumulants over sliding window and its application in speech endpoint detection

Regarding the performance of traditional endpoint detection algorithms degrades as the environment noise level increases, a recursive calculating algorithm for higher-order cu- mulants over a sliding window is proposed. Then it is applied to the speech endpoint detection. Furthermore, endpoint detection is carried out with the feature of energy. Experimental results show that both the computational efficiency and the robustness against noise of the proposed algorithm are improved remarkably compared with traditional algorithm. The average prob- ability of correct point detection （Pc-point） of the proposed voice activity detection （VAD） is 6.07% higher than that of G.729b VAD in different noisy at different signal-noise ratios （SNRs） environments.

Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions

We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions.Through analytical derivation,we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space.The theoretical conclusions are supported by a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method.The valid averaged efficiency is found to suppress the statistical uncertainties of the reproduced cumulants dramatically.Thus,usage of the averaged efficiency requires a careful study of phase space dependence.This study is important for carrying out precision measurements of higher-order cumulants in heavy-ion collision experiments at present and in future.

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.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

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.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

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.

A Study of a Moral Dilemma Stories Teaching Model Focusing on the Development of Higher-Order Thinking --"Synthetic polymers" as an example

Cultivating students'higher-order thinking is one of the important goals of modern education,and innovative teaching model is an effective way to achieve this goal.Aiming at the inadequacy of the existing moral dilemma stories approach in the transformation of knowledge and behavior,this research constructs a new Project Based Learning-Ethical Dilemma Stories(PBL-EDS)Teaching Model applicable to China's secondary education stage based on the innovative features of the moral dilemma stories approach on the core competencies,taking the chemistry subject as an example to carry out practice,and puts forward suggestions for the implementation of the teaching model.Chemistry as an example to carry out the practice,and suggestions are made for the implementation of the teaching model.

Identification of multiple inputs single output errors-in-variables system using cumulant

A higher-order cumulant-based weighted least square（HOCWLS） and a higher-order cumulant-based iterative least square（HOCILS） are derived for multiple inputs single output（MISO） errors-in-variables（EIV） systems from noisy input/output data. Whether the noises of the input/output of the system are white or colored, the proposed algorithms can be insensitive to these noises and yield unbiased estimates. To realize adaptive parameter estimates, a higher-order cumulant-based recursive least square（HOCRLS） method is also studied. Convergence analysis of the HOCRLS is conducted by using the stochastic process theory and the stochastic martingale theory. It indicates that the parameter estimation error of HOCRLS consistently converges to zero under a generalized persistent excitation condition. The usefulness of the proposed algorithms is assessed through numerical simulations.

基于RARE-Cumulant的互耦校正和DOA估计

基于四阶累计量及RARE(RAnk reducee quation)变换,结合均匀线阵互耦矩阵的特殊性,提出了一种新的互耦校正及波达方向估计算法。虽然四阶累计量比传统的二阶方法算法复杂,却扩展了阵列孔径,提高了在色噪声背景下DOA估计精度,而互耦系数并未因增加了虚拟阵元而增多。RARE变换将互耦系数与波达方向参量分离,有效地实现了多维参数估计的降维处理,减小了多维参量估计的计算量。仿真实验表明,在高斯色噪声背景下,本文方法计算量小,而且估计能力明显优于二阶去耦算法和传统的四阶方法。

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.

APPLICATIONS OF HIGHER-ORDER UPWIND SCHEME FOR PROJECTILES IN TRANSONIC FLOW

针对弹丸跨音速粘性绕流流场进行了数值仿真研究，并与实验进行了对比。数值仿真的控制方程为雷诺平均的Navier-Stokes方程，湍流模型采用Baldwin-Lomax模型，应用了四阶的MUSCL TVD格式。结果表明，该方法可以取得高清晰度的流场结构。

CLASSIFICATION OF GEAR FAULTS USING HIGHER-ORDER STATISTICS AND SUPPORT VECTOR MACHINES

Gears alternately mesh and detach in driving process, and then workingconditions of gears are alternately changing, so they are easy to be spalled and worn. But becauseof the effect of additive gaussian measurement noises, the signal-to-noises ratio is low; theirfault features are difficult to extract. This study aims to propose an approach of gear faultsclassification, using the cumulants and support vector machines. The cumulants can eliminate theadditive gaussian noises, boost the signal-to-noises ratio. Generalisation of support vectormachines as classifier, which is employed structural risk minimisation principle, is superior tothat of conventional neural networks, which is employed traditional empirical risk minimisationprinciple. Support vector machines as the classifier, and the third and fourth order cumulants asinput, gears faults are successfully recognized. The experimental results show that the method offault classification combining cumulants with support vector machines is very effective.

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.

Fission and Fusion of Localized Coherent Structures for a Higher-Order Broer-Kaup System

Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.

CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS

A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.

Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.