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.

Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises

It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker-Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation time and strength of coloured cross-correlated white noises on the upper bound.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon＇s information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

The diffusion in a harmonic oscillator driven by coloured noises ξ（t） and η（t） with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1） The curves of d versus noise intensity D and d versus noises cross-correlation time z3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient A of the two Ornstein-Uhlenbeck （O-U） noises. 2） Changing the value of T3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3） Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.

Intensity Correlation Time of a Single-Mode Laser Driven by Two Coloured Noises with Coloured Cross-Correlation with Bias Signal Modulation

The intensity correlation time T is studied by employing a gain-noise model of a single-mode laser driven by coloured pump noise τ1 and coloured quantum noise τ2 with coloured cross-correlation τ3 with a bias signal modulation. By using the linear approximation method, we detect that a maximum （i.e. resonance） exists in the curves of the intensity correlation time T versus the noise intensities D and Q when the noise correlation coefficient A is positive; and a minimum （i.e. suppression） exists in the T - D and T - Q curves when A is negative. When A is zero, T increases monotonously with increase of D and decreases monotonically with increase of Q. Furthermore, the curve of T versus the pump noise self-correlation time τ1 is also studied. Our study shows that, no matter what the value of A is, there exist one maximum and one minimum in the T - τ1 curve.

Time correction of the ocean bottom seismometers deployed at the southwest Indian ridge using ambient noise cross-correlation

Seismic monitoring using ocean bottom seismometers（OBS） is an efficient method for investigating earthquakes in mid-ocean ridge far away from land. Clock synchronization among the OBSs is difficult without direct communication because electromagnetic signals cannot propagate efficiently in water. Time correction can be estimated through global positioning system（GPS） synchronization if clock drift is linear before and after the deployment. However, some OBSs in the experiments at the southwest Indian ridge（SWIR） on the Chinese DY125-34 cruise had not been re-synchronized from GPS after recovery. So we attempted to estimate clock drift between each station pairs using time symmetry analysis（TSA） based on ambient noise cross-correlation. We tested the feasibility of the TSA method by analyzing daily noise cross-correlation functions（NCFs） that extract from the data of another OBS experiment on the Chinese DY125-40 cruise with known clock drift and the same deployment site. The results suggest that the NCFs＇ travel time of surface wave between any two stations are symmetrical and have an opposite growing direction with the date. The influence of different band-pass filters,different components and different normalized methods was discussed. The TSA method appeared to be optimal for the hydrophone data within the period band of 2–5 s in dozens of km-scale interstation distances. A significant clock drift of ~2 s was estimated between OBSs sets through linear regression during a 108-d deployment on the Chinese cruise DY125-34. Time correction of the OBS by the ambient noise cross-correlation was demonstrated as a practical approach with the appropriate parameters in case of no GPS re-synchronization.

Public cloud computing for seismological research:Calculating large-scale noise cross-correlations using ALIYUN

The amount of seismological data is rapidly increasing with accumulating observational time and increasing number of stations, requiring modern technique to provide adequate computing power. In present study, we proposed a framework to calculate large-scale noise crosscorrelation functions(NCFs) using public cloud service from ALIYUN. The entire computation is factorized into small pieces which are performed parallelly on specified number of virtual servers provided by the cloud. Using data from most seismic stations in China, five NCF databases are built. The results show that, comparing to the time cost using a single server, the entire time can be reduced over two orders of magnitude depending number of evoked virtual servers. This could reduce computation time from months to less than 12 hours. Based on obtained massive NCFs, the global body waves are retrieved through array interferometry and agree well with those from earthquakes. This leads to a solution to process massive seismic dataset within an affordable time and is applicable to other large-scale computing in seismological researches.

Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model

An approximate Fokker-Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution （SPD） and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ is in -1 〈λ≤0 and can be the double extrema in 0〈λ〈1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, （x）, versus λ The position and the value of the minimum are controlled by the noise-correlated times.

Composition of high frequency ambient noise from cross-correlation:A case study using a small aperture array

Long-time cross correlation of ambient noise has been proved as a powerful tool to extract Green＇s function between two receivers. The study of composition of ambient noise is important for a better understanding of this method. Previous studies confirm that ambient noise in the long period （3 s and longer） mostly consists of surface wave, and 0.25-2.5 s noise consists more of body waves. In this paper, we perform cross correlation processing at much higher frequency （30-70 Hz） using ambient noise recorded by a small aperture array. No surface waves emerge from noise correlation function （NCF）, but weak P waves emerge. The absence of surface wave in NCF is not due to high attenuation since surface waves are strong from active source, therefore probably the high ambient noise mostly consists of body wave and lacks surface wave. Origin of such high frequency body waves in ambient noise remains to be studied.

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.

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.

Stochastic resonance in a stochastic bistable system with additive noises and square-wave signal

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated.

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.

A Method of Eliminating Noises in Web Pages by Style Tree Model and Its Applications

A Web page typically contains many information blocks. Apart from the main content blocks, it usually has such blocks as navigation panels, copyright and privacy notices, and advertisements. We call these blocks the noisy blocks. The noises in Web pages can seriously harm Web data mining. To the question of climinating these noises, we intro duce a new tree structure, called Style Tree, and study an algorithm how to construct a site style tree. The Style Tree Model is employed to detect and climinate noises in any Web pages of the site. An information based measure to determine which element node is noisy is also constructed. In addition, the applications of this method are discussed in detail. Experimental results show that our noises climination technique is able to improve the mining results significantly. Key words noises climination - DOM tree - style tree - Web mining CLC number TP 339 Foundation item: Supported by the National Natural Science Foundation of China (60003013)Biography: ZHAN Cheng-li (1979-), male, Master candidate, research direction: Intelligent Information System.

On aerodynamic noises radiated by the pantograph system of high-speed trains

Pantograph system of high-speed trains become significant source of aerodynamic noise when travelling speed exceeds 300 km/h. In this paper, a hybrid method of non-linear acoustic solver （NLAS） and Ffowcs Williams-Hawkings （FW-H） acoustic analogy is used to predict the aerodynamic noise of pantograph system in this speed range. When the simulation method is validated by a benchmark problem of flows around a cylinder of finite span, we calculate the near flow field and far acoustic field surrounding the pantograph system. And then, the frequency spectra and acoustic attenuation with distance are analyzed, showing that the pantograph system noise is a typical broadband one with most acoustic power restricted in the medium-high frequency range from 200 Hz to 5 kHz. The aerodynamic noise of pantograph systems radiates outwards in the form of spherical waves in the far field. Analysis of the overall sound pressure level （OASPL） at different speeds exhibits that the acoustic power grows approximately as the 4th power of train speed. The comparison of noise reduction effects for four types of pantograph covers demonstrates that only case 1 can lessen the total noise by about 3 dB as baffles on both sides can shield sound wave in the spanwise direction. The covers produce additional aerodynamic noise themselves in the other three cases and lead to the rise of OASPLs.

Local-scale cross-correlation of seismic noise from the Calico fault experiment

Most studies of seismic noise cross-correlation （NCC） have focused on regional/continental scale imaging using empirical surface-wave Green＇s functions extracted from primary （0.05-0.08 Hz） and secondary （0.1-0.16 Hz） microseisms. In this work, we present the NCC results at higher frequencies （〉0.5 Hz） from 6 months seismic noise recorded by a local array （ - 4 km aperture） deployed along the Calico fault in the Mojave Desert, California. Both fast and slow propagating waves are observed from the NCC record-sections. We compare the NCCs from sensor pairs that share a common sensor with the records of a borehole shot located very close to this common sensor. The result shows a good match of the slow surface-wave arrivals, indicating that the NCC method is able to recover unbiased surface-wave Green＇s functions at local scales. The strong body-wave NCC component is caused by the P waves generated offshore California. Along a SW-NE profile across the fault, we observe apparent P-wave arrivals and their reflections, which can be explained by a low-velocity- zone （LVZ） along the Calico fault. We calculat6 the LVZ width to be - 2.3 kin, and the P-wave velocity reduction within the LVZ to be -35 %. These estimates are consistent with other evidence for a relatively wide LVZ along the Calico fault.

Noises and Signal-to-Noise Ratio of Nanosize EIS and ISFET Biosensors

The results of comparative theoretical analyzes of the behavior of internal low-frequency noises, signal-to-noise ratio and sensitivity to DNA molecules for EIS and ISFET based nanosize biosensors are presented. It is shown that EIS biosensor is more sensitive to the presence of DNA molecules in aqueous solution than ISFET sensor. Internal electrical noises level decreases with the increase of concentration of DNA molecules in aqueous solution. In the frequency range 10−3 - 103 Hz noises level for EIS sensor about in three orders is higher than for ISFET sensor. In the other hand, signal-to-noise ratio for capacitive EIS biosensor is much higher than for ISFET sensor.

Asymptotic Behavior of the Drift Coefficient Estimator of Stochastic Differential Equations Driven by Small Noises

The parametric estimation problem for diffusion processes with small white noise based on continuous time observations is well developed. However,in parametric inference,it is more realistic and interesting to consider asymptotic estimation for diffusion processes based on discrete observations. The least squares method is used to obtain the estimator of the drift parameter for stochastic differential equations( SDEs) driven by general Lévy noises when the process is observed discretely. Its strong consistency and the rate of convergence of the squares estimator are studied under some regularity conditions.

Statistical Properties of the Output Light Intensity in a Single-Mode Laser Driven by Correlated Noises

By using linear approximation we derive expressions for the correlation function,power spectrum and correlation time of the output light intensity in a single-mode laser driven by additive white noise and multiplicative colored noise with an exponential correlation form.The effects of correlation strength and correlation time of the noises on the above quantities are discussed and compared with the case of a delta function correlation form for the noises.

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.