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.

NUMERICAL ANALYSIS FOR STOCHASTIC TIME-SPACE FRACTIONAL DIFFUSION EQUATION DRIVEN BY FRACTIONAL GAUSSIAN NOISE

In this paper,we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussian noise with Hurst index H∈(1/2,1).A sharp regularity estimate of the mild solution and the numerical scheme constructed by finite element method for integral fractional Laplacian and backward Euler convolution quadrature for Riemann-Liouville time fractional derivative are proposed.With the help of inverse Laplace transform and fractional Ritz projection,we obtain the accurate error estimates in time and space.Finally,our theoretical results are accompanied by numerical experiments.

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.

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).

Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation

A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change, compatible to the electron transfer process governed by atomic packing density model. We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively, and introduce the coupling effect coming from both fluctuations and equilibrium variances. The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived, based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique. We explicitly elaborate the short time and long time approximations. The relationship between the two-diraensional description and the one-dimensional theory is also discussed.

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.