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.

Large Deviation Principle for the Fourth-order Stochastic Heat Equations with Fractional Noises

In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method.

Stochastic partial differential equations with gradient driven by space-time fractional noises

We establish a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises, where we suppose that the drfit term contains a gradient and satisfies certain non-Lipschitz condition. We prove the strong existence and uniqueness and joint Hölder continuity of the solution to the SPDEs.

The High-order SPDEs Driven by Multi-parameter Fractional Noises

The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.

The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order a.>1 driven by a fractional noise.We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle.The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of p-moment under some suitable assumptions.

Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise

The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.

Asymptotic analysis parabolic stochastic equations driven by of a kernel estimator for partial differential fractional noises

We study a strongly elliptic partial differential operator with time- varying coefficient in a parabolic diagonalizable stochastic equation driven by fractional noises. Based on the existence and uniqueness of the solution, we then obtain a kernel estimator of time-varying coefficient and the convergence rates. An example is given to illustrate the theorem.

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).

Reliability of quasi integrable and non-resonant Hamiltonian systems under fractional Gaussian noise excitation

The reliability of quasi integrable and non-resonant Hamiltonian system under fractional Gaussian noise(fGn)excitation is studied.Noting rather flat fGn power spectral density(PSD)in most part of frequency band,the fGn is innovatively regarded as a wide-band process.Then,the stochastic averaging method for quasi integrable Hamiltonian systems under wide-band noise excitation is applied to reduce 2n-dimensional original system into n-dimensional averaged ltd stochastic differential equations(SDEs).Reliability function and mean first passage time are obtained by solving the associated backward Kolmogorov equation and Pontryagin equation.The validity of the proposed procedure is tested by applying it to an example and comparing the numerical results with those from Monte Carlo simulation.

Fractional Brownian Motion and Sheet as White Noise Functionals

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.

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.

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.

The Stochastic Wave Equations Driven by Fractional and Colored Noises

We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a continuity modulus of the solution, and the HSlder continuity is presented.

A maximum noise fraction transform with improved noise estimation for hyperspectral images

Feature extraction is often performed to reduce spectral dimension of hyperspectral images before image classification. The maximum noise fraction （MNF） transform is one of the most commonly used spectral feature extraction methods. The spectral features in several bands of hyperspectral images are submerged by the noise. The MNF transform is advantageous over the principle component （PC） transform because it takes the noise information in the spatial domain into consideration. However, the experiments described in this paper demonstrate that classification accuracy is greatly influenced by the MNF transform when the ground objects are mixed together. The underlying mechanism of it is revealed and analyzed by mathematical theory. In order to improve the performance of classification after feature extraction when ground objects are mixed in hyperspectral images, a new MNF transform, with an improved method of estimating hyperspectral image noise covariance matrix （NCM）, is presented. This improved MNF transform is applied to both the simulated data and real data. The results show that compared with the classical MNF transform, this new method enhanced the ability of feature extraction and increased classification accuracy.

Lithological Discrimination of the Mafic-Ultramafic Complex, Huitongshan, Beishan, China: Using ASTER Data

The Beishan area has more than seventy mafic-ultramafic complexes sparsely distributed in the area and is of a big potential in mineral resources related to mafic-ultramafic intrusions. Many mafic-ultramafic intrusions which are mostly in small sizes have been omitted by previous works. This research takes Huitongshan as the study area, which is a major district for mafic-ultramafic occurrences in Beishan. Advanced spaceborne thermal emission and reflection radiometer（ASTER） data have been processed and interpreted for mapping the mafic-ultramafic complex. ASTER data were processed by different techniques that were selected based on image reflectance and laboratory emissivity spectra. The visible near-infrared（VNIR） and short wave infrared（SWIR） data were transformed using band ratios and minimum noise fraction（MNF）, while the thermal infrared（TIR） data were processed using mafic index（MI） and principal components analysis（PCA）. ASTER band ratios（6/8, 5/4, 2/1） in RGB image and MNF（1, 2, 4） in RGB image were powerful in distinguishing the subtle differences between the various rock units. PCA applied to all five bands of ASTER TIR imagery highlighted marked differences among the mafic rock units and was more effective than the MI in differentiating mafic-ultramafic rocks. Our results were consistent with information derived from local geological maps. Based on the remote sensing results and field inspection, eleven gabbroic intrusions and a pyroxenite occurrence were recognized for the first time. A new geologic map of the Huitongshan area was created by integrating the results of remote sensing, previous geological maps and field inspection. It is concluded that the workflow of ASTER image processing, interpretation and ground inspection has great potential for mafic-ultramafic rocks identifying and relevant mineral targeting in the sparsely vegetated arid region of northwestern China.

On-line Modeling of Non-stationary Network Traffic with Schwarz Information Criterion

Modeling of network traffic is a fundamental building block of computer science. Measurements of network traffic demonstrate that self-similarity is one of the basic properties of the network traffic possess at large time-scale. This paper investigates the change of non-stationary self-similarity of network traffic over time,and proposes a method of combining the discrete wavelet transform (DWT) and Schwarz information criterion (SIC) to detect change points of self-similarity in network traffic. The traffic is segmented into pieces around changing points with homogenous characteristics for the Hurst parameter,named local Hurst parameter,and then each piece of network traffic is modeled using fractional Gaussian noise (FGN) model with the local Hurst parameter. The presented experimental performance on data set from the Internet Traffic Archive (ITA) demonstrates that the method is more accurate in describing the non-stationary self-similarity of network traffic.