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.

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.

Stationary properties of a single-mode laser system with non-Gaussian and Gaussian noise

A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the stationary probability distribution function （SPDF） is derived. The SPDF as a function of the laser intensity exhibits a maximum, The maximum becomes smaller with the increase of the correlation intensity or the non-Gaussian parameter, where the later is a measure of the deviation from the Gaussian characteristic. The maximum becomes larger as the correlation time increases. The laser intensity stationary mean value decreases with the increase of the correlation intensity or the non-Gaussian parameter while increases with the correlation time increasing. The laser intensity normalized variance increases with the increase of the correlation intensity or the non-Gaussian parameter while decreases as the correlation time increases.

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.

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.

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.

Revisiting the nonlinear Gaussian noise model for hybrid fiber spans

We rederive from first principles and generalize the theoretical framework of the nonlinear Gaussian noise model to the case of coherent optical systems with multiple fiber types per span and ideal Nyquist spectra.We focus on the accurate numerical evaluation of the integral for the nonlinear noise variance for hybrid fiber spans.This task consists in addressing four computational aspects:(1)Adopting a novel transformation of variables(other than using hyperbolic coordinates)that changes the integrand to a more appropriate form for numerical quadrature;(2)Evaluating analytically the integral at its lower limit,where the integrand presents a singularity;(3)Dividing the interval of integration into subintervals of size and approximating the integral over each subinterval by using various algorithms;and(4)Deriving an upper bound for the relative error when the interval of integration is truncated in order to accelerate computation.We apply the proposed analytical model to the performance evaluation of coherent optical communications systems with hybrid fiber spans composed of quasi-single-mode and single-mode fiber segments.More specifically,the model is used to optimize the lengths of the optical fiber segments that compose each span in order to maximize the system performance.We check the validity of the optimal fiber segment lengths per span provided by the analytical model by using Monte Carlo simulation,where the Manakov equation is solved numerically using the split-step Fourier method.We show that the analytical model predicts the lengths of the optical fiber segments per span with satisfactory accuracy so that the system performance,in terms of the Q-factor,is within 0.1 dB from the maximum given by Monte Carlo simulation.

Formation and instability of spiral wave induced by Gaussian coloured noise

In this paper, we studied the effect of Gaussian coloured noise on the formation and instability of spiral waves described by one class of modified FitzHugh Nagumo equation. It was found that Gaussian coloured noise plays a constructive role in the formation, transition and instability of spiral wave. Too weak or too strong noise may act against the formation of spiral waves. At a certain noise level, spiral wave is maintained in a medium, in which spiral wave cannot be observed in the absence of the noise. It is difficult to make a stable spiral wave into unstable state by Gaussian coloured noise, unless the noise level is very high. The parameter regions of Gaussian coloured noise for spiral forming and spiral instability were given and discussed with numerical simulations.

Nano-friction phenomenon of Frenkel-Kontorova model under Gaussian colored noise

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova(FK)model under Gaussian colored noise is investigated by using the molecular dynamic simulation method.The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method.Via the stochastic Runge-Kutta algorithm,the relationship between different parameter values of the Gaussian colored noise(the noise intensity and the correlation time)and the nano-friction phenomena such as hysteresis,the maximum static friction force is separately studied here.Similar results are obtained from the two geometrically opposed ideal cases:incommensurate and commensurate interfaces.It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force,the introduction of noise can accelerate the motion of the system,making the atoms escape from the substrate potential well more easily.Interestingly,suitable correlation time and noise intensity give rise to super-lubricity.It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

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.

Improving the Transmission Security of Vein Images Using a Bezier Curve and Long Short-Term Memory

The act of transmitting photos via the Internet has become a routine and significant activity.Enhancing the security measures to safeguard these images from counterfeiting and modifications is a critical domain that can still be further enhanced.This study presents a system that employs a range of approaches and algorithms to ensure the security of transmitted venous images.The main goal of this work is to create a very effective system for compressing individual biometrics in order to improve the overall accuracy and security of digital photographs by means of image compression.This paper introduces a content-based image authentication mechanism that is suitable for usage across an untrusted network and resistant to data loss during transmission.By employing scale attributes and a key-dependent parametric Long Short-Term Memory(LSTM),it is feasible to improve the resilience of digital signatures against image deterioration and strengthen their security against malicious actions.Furthermore,the successful implementation of transmitting biometric data in a compressed format over a wireless network has been accomplished.For applications involving the transmission and sharing of images across a network.The suggested technique utilizes the scalability of a structural digital signature to attain a satisfactory equilibrium between security and picture transfer.An effective adaptive compression strategy was created to lengthen the overall lifetime of the network by sharing the processing of responsibilities.This scheme ensures a large reduction in computational and energy requirements while minimizing image quality loss.This approach employs multi-scale characteristics to improve the resistance of signatures against image deterioration.The proposed system attained a Gaussian noise value of 98%and a rotation accuracy surpassing 99%.

A Novel Coding Method Based on Fuzzy Vector Quantization for Noised Image

In this paper a novel coding method based on fuzzy vector quantization for noised image with Gaussian white-noise pollution is presented. By restraining the high frequency subbands of wavelet image the noise is significantly removed and coded with fuzzy vector quantization. The experimental result shows that the method can not only achieve high compression ratio but also remove noise dramatically.

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio （SNR） of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.

Noise level estimation method with application to EMD-based signal denoising

This paper proposes a new signal noise level estimation approach by local regions. The estimated noise variance is applied as the threshold for an improved empirical mode decomposition（EMD） based signal denoising method. The proposed estimation method can effectively extract the candidate regions for the noise level estimation by measuring the correlation coefficient between noisy signal and a Gaussian filtered signal. For the improved EMD based method, the situation of decomposed intrinsic mode function（IMFs） which contains noise and signal simultaneously are taken into account. Experimental results from two simulated signals and an X-ray pulsar signal demonstrate that the proposed method can achieve better performance than the conventional EMD and wavelet transform（WT） based denoising methods.

NOISE-INDUCED CHAOTIC MOTIONS IN HAMILTONIAN SYSTEMS WITH SLOW-VARYING PARAMETERS

This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.

Influence of the colored noise on determining the period of a torsion pendulum

Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ？t/（1/λ） where ？t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ？t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ？t/（1/λ） is less than 1, the uncertainty remains substantially unchanged.

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).

Validity of non-local mean filter and novel denoising method

Background Image denoising is an important topic in the digital image processing field.This study theoretically investigates the validity of the classical nonlocal mean filter(NLM)for removing Gaussian noise from a novel statistical perspective.Method By considering the restored image as an estimator of the clear image from a statistical perspective,we gradually analyze the unbiasedness and effectiveness of the restored value obtained by the NLM filter.Subsequently,we propose an improved NLM algorithm called the clustering-based NLM filter that is derived from the conditions obtained through the theoretical analysis.The proposed filter attempts to restore an ideal value using the approximately constant intensities obtained by the image clustering process.In this study,we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components.Result The experiment yields improved peak signal-to-noise ratio values and visual results upon the removal of Gaussian noise.Conclusion However,the considerable practical performance of our filter demonstrates that our method is theoretically acceptable as it can effectively estimate ideal images.