Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.

Current transport and mass separation for an asymmetric fluctuation system with correlated noises

We discuss the transport of an underdamped particle driven by an external fluctuation force in a spatially periodic asymmetric potential with correlated noises. The corresponding mathematical model is established. The movement of the steady current of an underdamped particle is presented by the method of the numerical simulation. It is indicated that the value of the current may be negative, zero, or positive. The external fluctuation force and correlated noises can effect the current direction. Under the appropriate parameters, the correlated noises intensity may even raise a reversal of the current. Besides, we have noticed a phenomenon that particles with different weight have different directions during movement by the impact of the correlated noises and external fluctuation force. Therefore, the Brownian particles can be effectively separated according to their masses.

Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.

Convergence Analysis of Splitting-Up Algorithm of the Zakai’s Equation with Correlated Noises

In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s equation.The splitting-up algorithm has been first studied in the independent noises case by Bensoussan,et al.(1990).In this paper,the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises’case.Given a time discretization,one splits the solution of the Zakai’s equation into two interlacing processes(with possibly computational advantage).These two processes correspond respectively to the prediction and updating.Under certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to zero.The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence.The major technical difficulty in the correlated noises’case,compared with the independent case,is to control the gradient of the second process in some sense.To illustrate the potentially computational advantage of the schemes based on the splitting-up ways,the authors experiment on a toy NLF model using the feedback particle filter(FPF)developed based on the splitting-up method and the sampling importance and resampling(SIR)as comparison.The FPF outperforms in both accuracy and efficiency.

A Denoiser for Correlated Noise Channel Decoding: Gated-Neural Network

This letter proposes a sliced-gated-convolutional neural network with belief propagation(SGCNN-BP) architecture for decoding long codes under correlated noise. The basic idea of SGCNNBP is using Neural Networks(NN) to transform the correlated noise into white noise, setting up the optimal condition for a standard BP decoder that takes the output from the NN. A gate-controlled neuron is used to regulate information flow and an optional operation—slicing is adopted to reduce parameters and lower training complexity. Simulation results show that SGCNN-BP has much better performance(with the largest gap being 5dB improvement) than a single BP decoder and achieves a nearly 1dB improvement compared to Fully Convolutional Networks(FCN).

Simulation study of the two-time intensity correlation function of a two-mode laser system with both pump and quantum noises

This paper investigates the two-time intensity correlation function of a two-mode ring laser system subjected to both pump and quantum noises by stochastic simulation. It finds that the decay rate of the intensity correlation function of one mode gets faster with decreasing values of relevant parameters, i.e., the coupling constant ξ, the cross-correlation coefficient A, the difference of the pump parameters Aa and the pump parameter al; however, its variations get complex in the other mode when relevant parameters are changed. The investigating results also show that the effects of the mode competition on intensity correlation function are obvious.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance （ESR） in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio （SNR） is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.

Dense coding capacity in correlated noisy channels with weak measurement

Capacity of dense coding via correlated noisy channel is greater than that via uncorrelated noisy channel.It is shown that the weak measurement and reversal measurement need to further improve their quantum dense coding capacity in correlated amplitude damping channel,but this improvement is very small in correlated phase damping channel and correlated depolarizing channel.

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh–Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh–Nagumo（FHN） neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation（DMA） and direct simulation（DS）. Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.

Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C（τ） and the associated relaxation time T（C） in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.

Monitoring of velocity changes based on seismic ambient noise: A brief review and perspective

Over the past two decades,the development of the ambient noise cross-correlation technology has spawned the exploration of underground structures.In addition,ambient noise-based monitoring has emerged because of the feasibility of reconstructing the continuous Green’s functions.Investigating the physical properties of a subsurface medium by tracking changes in seismic wave velocity that do not depend on the occurrence of earthquakes or the continuity of artificial sources dramatically increases the possibility of researching the evolution of crustal deformation.In this article,we outline some state-of-the-art techniques for noise-based monitoring,including moving-window cross-spectral analysis,the stretching method,dynamic time wrapping,wavelet cross-spectrum analysis,and a combination of these measurement methods,with either a Bayesian least-squares inversion or the Bayesian Markov chain Monte Carlo method.We briefly state the principles underlying the different methods and their pros and cons.By elaborating on some typical noisebased monitoring applications,we show how this technique can be widely applied in different scenarios and adapted to multiples scales.We list classical applications,such as following earthquake-related co-and postseismic velocity changes,forecasting volcanic eruptions,and tracking external environmental forcing-generated transient changes.By monitoring cases having different targets at different scales,we point out the applicability of this technology for disaster prediction and early warning of small-scale reservoirs,landslides,and so forth.Finally,we conclude with some possible developments of noise-based monitoring at present and summarize some prospective research directions.To improve the temporal and spatial resolution of passive-source noise monitoring,we propose integrating different methods and seismic sources.Further interdisciplinary collaboration is indispensable for comprehensively interpreting the observed changes.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

Equipartition and retrieval of Green's function

Physical and mathematical arguments are presented for equipartition as the statistical state achieved by a ran- dom field, independent of its sources, in the limit of enough scattering. The arguments are simplest for the case of thermally excited fields, but are shown to apply also, with caveats, in non-equilibrium acoustics and seismology. Practical implications are discussed.

A WYNER-ZIV VIDEO CODING METHOD UTILIZING MIXTURE CORRELATION NOISE MODEL

In Wyner-Ziv (WZ) Distributed Video Coding (DVC), correlation noise model is often used to describe the error distribution between WZ frame and the side information. The accuracy of the model can influence the performance of the video coder directly. A mixture correlation noise model in Discrete Cosine Transform (DCT) domain for WZ video coding is established in this paper. Different correlation noise estimation method is used for direct current and alternating current coefficients. Parameter estimation method based on expectation maximization algorithm is used to estimate the Laplace distribution center of direct current frequency band and Mixture Laplace-Uniform Distribution Model (MLUDM) is established for alternating current coefficients. Experimental results suggest that the proposed mixture correlation noise model can describe the heavy tail and sudden change of the noise accurately at high rate and make significant improvement on the coding efficiency compared with the noise model presented by DIStributed COding for Video sERvices (DISCOVER).

Temporal variation of noise correlation function(NCF) in Beijing and surroundings:Its relation with climate events and implications

Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.

Teleseismic body waves extracted from ambient noise cross correlation between F-net and Chin Array phase Ⅱ

The vertical-vertical noise cross-correlation functions(NCFs)between two seismic arrays,the Japan F-net and Chin Array phase Ⅱ,are calculated using continuous recordings during 2013-2016.After array interferometry to obtain bin stacked NCFs,clear body waves are retrieved at different period bands.Teleseismic direct P waves for distance 15-40 degrees are observed between short period 3-10 s while core reflected PcP/ScS waves are more obvious for longer period 30-60 s.The signal-to-noise-ratio(SNR)of the short period P waves reaches its highest point with bin widths around 20 km while SNRs of PcP and ScS increase slowly with bin width.All those body waves demonstrate clear directivity with strong signals traveling from the east.The time-lapse SNR variations for the PcP and ScS show correlation with the occurrence of major earthquakes,while the P-wave SNR demonstrates seasonal variations with additional contribution from major earthquakes.The present results suggest teleseismic body waves can be retrieved through bin stacking,though further processing is still necessary to obtain finer waveforms such as P wave triplications.

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.

State Fusion Estimation for Multilevel Multisensor System

Based on the single sensor Kalman filtering equations, this paper presents two-level and three-level optimal centralized and distributed estimation algorithms for hierarchical multisensor systems. The solution shows that when the correlated matrix, the mean of noise, the control input, and the measurement error are all zero, the result in this paper turns out to be the standard algorithm discussed. Simulation shows that the mean of noise, the control input, and the measurement error will not change the estimation covariance and the estimation covariance fluctuates greatly when the cross-correlated matrix is similar to the covariance of process noise.

Experimental Study of Acoustic Noise Correlation Technique for Passive Monitoring of Rails

The work presented in this paper aims at investigating the ability of acoustic noise correlation technique for railway infrastructure health monitoring. The principle of this technique is based on impulse responses reconstruction by correlation of random noise propagated in the medium. Since wheel-rail interaction constitutes a source of such noise, correlation technique could be convenient for detection of rail defects using only passive sensors. Experiments have been carried out on a 2 m-long rail sample. Acoustic noise is generated in the sample at several positions. Direct comparison between an active emission-reception response and the estimated noise correlation function has confirmed the validity of the equivalence relation between them. The quality of the reconstruction is shown to be strongly related to the spatial distribution of the noise sources. High sensitivity of the noise-correlation functions to a local defect on the rail is also demonstrated. However, interpretation of the defect signature is more ambiguous than when using classical active responses. Application of a spatiotemporal Fourier transform on data recorded with variable sensor-defect distances has allowed overcoming this ambiguity.