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.

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 f Gn and related fractional Brownian motion(fBm) 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.

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.

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.

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.

Anti-Interference Study on Radiographic Bone Age Estimation Based on Artificial Intelligence Model

In this paper, the interferences of X-ray image noise on a bone age model, Xception model, were studied. We conduct a comparative experiment test according to the output performance of the neural network model using both the original image training and noise-added (Gaussian noise plus salt-pepper noise) training, and analyze the anti-interference ability of the Xception model, hoping to improve it through noise enhancement training and generalize the application ability of the model. The results show that the model trained with noise-added (Gaussian noise plussalt-pepper noise) images can make predictions that are more robust and less affected by the image disturbances, such as image noise.

Hopf bifurcation of nonlinear system with multisource stochastic factors

The article mainly explores the Hopf bifurcation of a kind of nonlinear system with Gaussian white noise excitation and bounded random parameter.Firstly,the nonlinear system with multisource stochastic fac-tors is reduced to an equivalent deterministic nonlinear system by the sequential orthogonal decomposi-tion method and the Karhunen-Loeve(K-L)decomposition theory.Secondly,the critical conditions about the Hopf bifurcation of the equivalent deterministic system are obtained.At the same time the influence of multisource stochastic factors on the Hopf bifurcation for the proposed system is explored.Finally,the theorical results are verified by the numerical simulations.

Predicting solutions of the stochastic fractional order dynamical system using machine learning

The solution of fractional-order systems has been a complex problem for our research.Traditional methods like the predictor-corrector method and other solution steps are complicated and cumbersome to derive,which makes it more difficult for our solution efficiency.The development of machine learning and nonlinear dynamics has provided us with new ideas to solve some complex problems.Therefore,this study considers how to improve the accuracy and efficiency of the solution based on traditional methods.Finally,we propose an efficient and accurate nonlinear auto-regressive neural network for the fractional order dynamic system prediction model(FODS-NAR).First,we demonstrate by example that the FODS-NAR algorithm can predict the solution of a stochastic fractional order system.Second,we compare the FODS-NAR algorithm with the famous and good reservoir computing(RC)algorithms.We find that FODS-NAR gives more accurate predictions than the traditional RC algorithm with the same system parameters,and the residuals of the FODS-NAR algorithm are closer to 0.Consequently,we conclude that the FODS-NAR algorithm is a method with higher accuracy and prediction results closer to the state of fractional-order stochastic systems.In addition,we analyze the effects of the number of neurons and the order of delays in the FODS-NAR algorithm on the prediction results and derive a range of their optimal values.

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.

Damage detection of 3D structures using nearest neighbor search method

An innovative damage identification method using the nearest neighbor search method to assess 3D structures is presented.The frequency response function was employed as the input parameters to detect the severity and place of damage in 3D spaces since it includes the most dynamic characteristics of the structures.Two-dimensional principal component analysis was utilized to reduce the size of the frequency response function data.The nearest neighbor search method was employed to detect the severity and location of damage in different damage scenarios.The accuracy of the approach was verified using measured data from an experimental test;moreover,two asymmetric 3D numerical examples were considered as the numerical study.The superiority of the method was demonstrated through comparison with the results of damage identification by using artificial neural network.Different levels of white Gaussian noise were used for polluting the frequency response function data to investigate the robustness of the methods against noise-polluted data.The results indicate that both methods can efficiently detect the damage properties including its severity and location with high accuracy in the absence of noise,but the nearest neighbor search method is more robust against noisy data than the artificial neural network.

SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS

This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.

Construction of Regular Rate-Compatible LDPC Convolutional Codes

In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.

Deep CNN Model for Multimodal Medical Image Denoising

In the literature,numerous techniques have been employed to decrease noise in medical image modalities,including X-Ray(XR),Ultrasonic(Us),Computed Tomography(CT),Magnetic Resonance Imaging(MRI),and Positron Emission Tomography(PET).These techniques are organized into two main classes:the Multiple Image(MI)and the Single Image(SI)techniques.In the MI techniques,images usually obtained for the same area scanned from different points of view are used.A single image is used in the entire procedure in the SI techniques.SI denoising techniques can be carried out both in a transform or spatial domain.This paper is concerned with single-image noise reduction techniques because we deal with single medical images.The most well-known spatial domain noise reduction techniques,including Gaussian filter,Kuan filter,Frost filter,Lee filter,Gabor filter,Median filter,Homomorphic filter,Speckle reducing anisotropic diffusion(SRAD),Nonlocal-Means(NL-Means),and Total Variation(TV),are studied.Also,the transform domain noise reduction techniques,including wavelet-based and Curvelet-based techniques,and some hybridization techniques are investigated.Finally,a deep(Convolutional Neural Network)CNN-based denoising model is proposed to eliminate Gaussian and Speckle noises in different medical image modalities.This model utilizes the Batch Normalization(BN)and the ReLU as a basic structure.As a result,it attained a considerable improvement over the traditional techniques.The previously mentioned techniques are evaluated and compared by calculating qualitative visual inspection and quantitative parameters like Peak Signal-to-Noise Ratio(PSNR),Correlation Coefficient(Cr),and system complexity to determine the optimum denoising algorithm to be applied universally.Based on the quality metrics,it is demonstrated that the proposed deep CNN-based denoising model is efficient and has superior denoising performance over the traditionaldenoising techniques.

MOTION ARTIFACT REDUCTION IN FUNCTIONAL NEAR INFRARED SPECTROSCOPY SIGNALS BY AUTOREGRESSIVE MOVING AVERAGE MODELING BASED KALMAN FILTERING

Functional near infrared spectrosecopy(NIRS)is a technique that is used for noninvasive measurement of the oxyhemoglobin(HbO_(2))and deoxyhemoglobin(HHb)concentrations in the brain tissue.Since the ratio of the concentration of these two agents is correlated with the neuronal activity,ONIRS can be usod for the monitoring and quantifying the cortical activity.The portability of NIRS makes it a good candidate for studies involving subject's movement.The NIRS measurements,however,are sensitive to artifacts generated by subject's head motion.This makes fNIRS signals less effective in such applications.In this paper,the autoregressive moving average(ARMA)modeling of the NIRS signal is proposed for state-space representation of the signal which is then fed to the Kalman filter for estimating the motionless signal from motion corrupted signal.Results are compared to the autoregressive model(AR)based approach,which has been done previously,and show that the ARMA models outperform AR models.We attribute it to the richer structure,containing more terms indeed,of ARMA than AR.We show that the signal to noise ratio(SNR)is about 2 dB higher for ARMA based method.

AN FFT-BASED SELF-SIMILAR TRAFFIC GENERATOR

The self similarity of the network traffic has great influences on the performance. But there are few analytical or even numerical solutions for such a model. So simulation becomes the most efficient method for research. Fractal Gaussian noise (FGN) is the most popularly used self similar model. This paper presented an FGN generator based on fast Fourier transform (FFT). The study indicates that this algorithm is fairly fast and accurate.