Inhibitory effect induced by fractional Gaussian noise in neuronal system

We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly,essential properties of fractional Brownian motion(fBm) and generation of fractional Gaussian noise(fGn) are presented,and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes.Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of f Gn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance(ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals(ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

一类由空间粗糙高斯噪声驱动分数阶动力学方程的性质研究

本文主要研究了一类空间粗糙高斯噪声驱动的分数阶动力学方程,其中高斯噪声关于时间是白色的,关于空间的相依结构由Hurst指数小于1/2的分数布朗运动的协方差刻画.基于Malliavin分析技巧,我们证明了该类方程温和解在Skorohod意义下的存在性.同时证明了其温和解矩的上、下界的估计.最后证明了其温和解关于时间和空间变量的Holder连续性.

fGn激励下非线性系统近似方法适用性的解析分析

由于受分数高斯噪声(fGn)激励的非线性系统响应不再具有马尔科夫性,基于扩散过程的理论方法不能直接用于研究此类问题。作为近似方法,宽带噪声激励的拟哈密顿系统随机平均法已经被用于解决此类问题。虽然,该理论方法在响应预测和可靠性分析方面取得了较好的效果,但是到目前为止还没有做过对近似方法的误差和适用性的解析分析。在本研究中,将近似方法用于分析fGn激励下的单自由度非线性系统,得到了系统响应的近似解析解,再结合已报道的精确解析解,用渐近分析的方法进行了误差分析,从而对近似方法的适用性进行了论证,为将来能够进一步扩展近似方法的应用提供了理论依据。

基于FGN和FLN的网络通信量模型FGLN

为了捕获大规模网络通信量的动力学行为特征,该文提出了一种基于分数高斯噪声和分数利维噪声的网络通信量新模型,给出了该模型参数的估计方法和通信量生成算法。仿真实验和对比分析表明,与其它经典通信量模型相比,新模型具有更好的性能,能够较好地捕获实际网络通信量的动力学行为特征,包括自相似性和冲激性。

fGn模型在结肠癌基因表达数据集去噪中的应用

基因表达数据集获取过程中容易掺杂噪声成分,噪声会干扰数据的正确表达从而影响其后期的分析与研究。基于中值计算法估计噪声标准差的经验模态分解(EMD)去噪存在一定的不足,从而影响去噪效果。分数阶高斯噪声(fGn)模型可提供EMD下较为准确的噪声标准差估计方法,在该模型下去噪可减少白色及有色噪声,进而增强去噪效果。因此在中值计算EMD去噪基础上,提出一种基于fGn模型的去噪方案,并对结肠癌基因表达数据集做去噪分析。实验结果表明,相比中值计算EMD去噪方法,改进方法的信噪比、噪声抑制比、t检验等值具有一定的优势,可作为基因表达数据集去噪的一种参考方案。

Stochastic response of fractional-order van der Pol oscillator

We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.

一种刻划浮动汇率的模型:增量一分数高斯噪声(I-FGN)过程

为了描述汇率变动之间的远程相关行为，本文提出了刻划浮动汇率的一种新模型并给出了具体的建模方法，实验结果说明该模型是有意义的．

Riemann-Liouville型分数阶导数的非线性估计

本文主要研究任意有界连续信号的Riemann-Liouville分数阶导数估计问题.当分数阶α属于0到1时,首先利用滑模技术提出一种有界连续信号分数阶导数的非线性估计方法;然后将其结果推广至分数阶α∈R+的情况,并给出相应的非线性估计方案.借助Riemann-Liouville分数阶微积分频率分布模型,本文详细分析讨论了所给分数阶导数非线性估计的收敛性问题,并得到相应闭环系统是渐近稳定的结论.文中所提方法的主要优点是在事先未知给定信号分数阶导数上界的情况下,不仅能自适应地估计其Riemann-Liouville分数阶导数,而且当信号中含有随机噪声和不确定扰动时依然能正常工作.数值仿真实例验证了本文所给估计方法的可行性和有效性.

基于FLOM和LSTM的频谱感知算法

为解决现有频谱感知检测方法在Alpha噪声中性能下降的问题,提出一种基于FLOM(fractional low order moment,FLOM)和LSTM(long short-term memory,LSTM)神经网络的频谱感知算法。利用分数低阶矩在解决非高斯噪声下感知性能退化的强大能力以及长短期记忆神经网络在解决时序特性问题上的强大处理能力,设计一个频谱感知算法。不同于现有的基于能量和协方差矩阵等二阶统计量的频谱感知,利用FLOM对数据进行分数低阶预处理后,LSTM通过提取分数低阶协方差矩阵的特征进行决策。仿真结果表明,该算法比传统的频谱感知算法具有更高的检测概率。在低信噪比下,基于分数低阶矩阵感知的LSTM检测方案的检测概率比其它基于数据驱动的检测方法改善了至少15%。

Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise

A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.

AN INFORMATIC APPROACH TO A LONG MEMORY STATIONARY PROCESS

Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data.Most of the definitions concerning the long memory of a stationary process are based on the second-order properties of the process.The mutual information between the past and future I_(p−f) of a stationary process represents the information stored in the history of the process which can be used to predict the future.We suggest that a stationary process can be referred to as long memory if its I_(p−f) is infinite.For a stationary process with finite block entropy,I_(p−f) is equal to the excess entropy,which is the summation of redundancies that relate the convergence rate of the conditional(differential)entropy to the entropy rate.Since the definitions of the I_(p−f) and the excess entropy of a stationary process require a very weak moment condition on the distribution of the process,it can be applied to processes whose distributions are without a bounded second moment.A significant property of I_(p−f) is that it is invariant under one-to-one transformation;this enables us to know the I_(p−f) of a stationary process from other processes.For a stationary Gaussian process,the long memory in the sense of mutual information is more strict than that in the sense of covariance.We demonstrate that the I_(p−f) of fractional Gaussian noise is infinite if and only if the Hurst parameter is H∈(1/2,1).

Stochastic averaging of quasi integrable and resonant Hamiltonian systems excited by fractional Gaussian noise with Hurst index 1/2

A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.

高斯白噪声激励下含分数阶PD控制器广义DVP系统的随机P-分岔

研究了高斯白噪声激励下含分数阶PD控制器广义DVP系统的随机P-分岔.依据均方最小误差原理将含分数阶PD控制器系统转化为等价的整数阶系统,利用随机平均法求得系统幅值的稳态概率密度函数,且分析了分数阶PD控制器的相关参数及系数对系统的影响,结合稳态概率密度函数曲线图发现改变其参数及系数会诱导系统发生随机P-分岔行为.

Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise

To model wave propagation in inhomogeneous media with frequency dependent power-law attenuation,it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time.The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative Gaussian noise and additive fractional Gaussian noise,because of the potential fluctuations of the external sources.The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation.First,the space-time multiplicative Gaussian noise and additive fractional Gaussian noise are discretized,which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense.We further present a complete regularity theory for the regularized equation.A standard finite element approximation is used for the spatial operator,and a mean-square priori estimates for the modeling error and the approximation error to the solution of the regularized problem are established.Finally,numerical experiments are performed to confirm the theoretical analysis.

经验模态分解阈值消噪方法及其在惯性导航系统数据处理中的应用

针对惯性元件误差中有色噪声影响远大于白噪声的情况,建立元件误差的分形高斯噪声模型,利用功率谱密度方法估计模型参数。基于噪声模型推导经验模分解(EMD)的各固有模态函数(IMF)分量中噪声的方差,以此估计各分量相应的阈值,建立EMD阈值消噪方法。将该方法应用于INS中,并与小波阈值法进行比较。结果表明,小波阈值法难以控制元件中有色噪声的影响,EMD阈值法与噪声模型紧密结合,能够更有效地削弱元件中的随机误差,提高INS精度。

基于分数阶小波域GSM模型的地震信号随机噪声压制方法

地震信号中的随机噪声是一种干扰波,严重降低了地震信号的信噪比,并影响着资料的后续处理和分析.本文根据地震信号中有效信号和随机噪声的差异,结合分数阶B样条小波变换与高斯尺度混合模型提出了一种地震信号随机噪声压制方法.首先利用分数阶B样条小波变换将含噪地震信号映射到最优分数阶小波时频域内,然后对各小波子带系数分别建立高斯尺度混合模型,由贝叶斯方法估计出源地震信号小波系数,最后使用分数阶B样条小波逆变换重构得到降噪后的地震信号.利用本文方法对合成地震记录和实际地震信号进行降噪处理,实验结果表明本文方法能够有效地压制地震信号中的随机噪声,并且较好地保留了有效信号.

基于经验模态分解空域相关滤波的脉冲星信号消噪

针对脉冲星信号信噪比极低,且信号中有色噪声成分远大于高斯白噪声的特点,提出了一种基于经验模态分解(empirical mode decomposition,EMD)的脉冲星信号空域相关滤波消噪方法。首先建立脉冲星信号的分形高斯噪声模型,根据双对数功率谱密度估计分形高斯噪声的Hurst参数值;然后,结合脉冲星累积信号的窗口辐射特性和分形高斯噪声经EMD分解后的噪声分布特点,估计脉冲星信号各层内蕴模态函数(intrinsic mode function,IMF)中噪声的方差;最后,以IMF噪声方差为基础,建立EMD空域相关滤波方法并应用于脉冲星累积轮廓消噪。实验结果表明,与经典的平移不变小波阈值消噪法、平移不变小波空域相关滤波消噪法以及EMD模态单元比例萎缩消噪法相比,改进的EMD空域相关滤波消噪法在抑制脉冲信号中的噪声和保留更多的微脉冲特征细节信息方面更加有效。

随机平均原理研究若干进展

本文介绍了随机平均原理的研究现状和发展趋势,探讨了基于非高斯列维噪声、分数高斯噪声、Markov切换的随机复杂动力学系统随机平均原理研究中的若干问题及进展.

具有自相似特性的业务及其对ATM网络性能的影响

近年来，通过对VBR视频速率、TCP/FTP分组到达及长度和以太网业务流量的大量统计，发现很多业务在本质上表现了自相似（或称分形）的特性，即在不同时间尺度上表现出结构的相似性。本文对自相似业务的定义、性质和生成方法进行了综述，讨论了自相似业务对ATM网络性能的影响。最后，指出了有待进一步深入研究的课题。