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.

The influence of observation environment on background noise level of gPhone gravimeter

Based on the observations of 36 gPhone gravimeters in 2015, the background noise levels in the seismic frequency band（200-600 s） and sub-seismic band（1-6 h） are calculated. The differences in the PSD（power spectrum density） of each band of gPhone gravimetric gauges in different surrounding environments were analyzed and compared with Peterson＇s NLNM（new low-noise model） which is derived from the envelope at the power spectrum density of 75 seismograph stations around the world. The results showed that： the influence of station type on the noise magnitude of gPhone gravimeter is very small; The seismic band noise magnitude（hereinafter referred to as SNM） and the sub-seismic band noise magnitude（hereinafter referred to as SSNM） in the coastal gPhone gravimeter are higher than those of inland stations. Although the local hydrological change has a great influence on the gravity observation, the rainfall is not directly relative to the noise magnitude of the instrument. Except 3 coastal stations, the eight stations which had the highest amplitudes in the SNM were located near the seismic belt. This indicates that the SNM of the gPhone Gravimeter may reflect some seismic information.Compared with the NLNM model, the PSD of the gPhone gravimeter is lower than the NLNM model in the long period band（〈3×10^（-5）Hz）, indicating that the gPhone gravimeter is more suitable for detecting long-period signals（〉10 h） than the seismometer.

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises:Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.

Time Dependence of Entropy Flux and Entropy Production of a Dissipative Dynamical System Driven by Non-Gaussian Noise

A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon＇s information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production.

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

Nonparametric VSS-APA based on precise background noise power estimate

The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.

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.

Performance Analysis of Outage Probability and Error Rate of Square M-QAM in Mobile Wireless Communication Systems over Generalized α-μ Fading Channels with Non-Gaussian Noise

This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.

ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LVY NOISES

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.

Entropic Resonant Activation and Stochastic Resonance Driven by Non-Gaussian Noise

The transition rate and stochastic resonance （SR） of a Brownian particle moving in a confined system under the presence of entropic barriers are investigated when the system is driven by non-Gaussian noise. The explicit expressions of the transition rate and the speetrai power amplification （SPA） are obtained, respectively. The effects of the parameter q indicating the departure from the Ganssian noise and the correlation time T of the non-Gaussian noise on the transition rate and the SPA are discussed. Research results show that： （i） The transition rate as a function of the noise strength exhibits a maximum. This maximum for transition rate identifies the phenomenon of entropie resonant activation （ERA）, the parameter q and the noise correlation time T weaken the ERA of the system; （ii） The curves of SPA appear a transition from one peak to double-peak, and then to one peak again as the noise correlation time T of non-Gaussian noise increases.

Effects of non-Gaussian noise on the dynamical properties of a logistic system

The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.

Ballistic diffusion induced by non-Gaussian noise

In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C（t） of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior：for q ≤ 1,C（t） is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 〉 1,C（t） can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C（t）,the particle exhibits a normal diffusion for q ≤ 1,while for q 〉 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads 〈[x（t）-]2∝t2.

The background noise level of vertical pendulum tiltmeter in China

By using the observation data of the vertical pendulum tiltmeter in China,the influence of different sampling rates on the results of power spectral density is studied,and the background noise level of the seismic frequency band(200-600 s)of different stations and different types of instruments is emphatically analyzed.The conclusions are as follows:1.The results of both single station and national statistics show that the noise levels of the two types of pendulum tiltmeter equal in the seismic frequency band;2.There is no obvious regularity in the regional distribution,due to the influence of ocean and active tectonic movement,the noise levels of some stations in coastal areas are relatively high;3,The curves of high noise level instrument are generally not smooth and burr-prone.Except for some stations affected by the ocean,they are mostly caused by the observation environment or the instrument itself.

Effects of non-Gaussian noise on a calcium oscillation system

We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum （Rmax） with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q （e.g., q = 0.9, q = 1.0）, R has a maximum with increasing correlation time t. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.

Hybrid In-Vehicle Background Noise Reduction for Robust Speech Recognition:The Possibilities of Next Generation 5G Data Networks

This pilot study focuses on employment of hybrid LMS-ICA system for in-vehicle background noise reduction.Modern vehicles are nowadays increasingly supporting voice commands,which are one of the pillars of autonomous and SMART vehicles.Robust speaker recognition for context-aware in-vehicle applications is limited to a certain extent by in-vehicle back-ground noise.This article presents the new concept of a hybrid system which is implemented as a virtual instrument.The highly modular concept of the virtual car used in combination with real recordings of various driving scenarios enables effective testing of the investigated methods of in-vehicle background noise reduction.The study also presents a unique concept of an adaptive system using intelligent clusters of distributed next generation 5G data networks,which allows the exchange of interference information and/or optimal hybrid algorithm settings between individual vehicles.On average,the unfiltered voice commands were successfully recognized in 29.34%of all scenarios,while the LMS reached up to 71.81%,and LMS-ICA hybrid improved the performance further to 73.03%.

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system.

State Estimation for Sound and Vibration Emitted from a Machine Based on Sound Measurement Under Existenceof Background Noise

Many studies on the diagnosis for machines have become important recently because of increased use of various complex industrial systems.The correlation information between sound and vibration is very important for machine diagnosis.Usually,vibration pickups are attached directly to the machine in order to measure vibration data.However,in some cases,the sensors can not be attached directly on highly precise devices.In this study,a method to estimate the fluctuation of sound and vibration is proposed based on the measurement data of sound emitted from the machine under existence of background noise.The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor.

GPR data noise attenuation on the curvelet transform

Signal extraction is critical in GRP data processing and noise attenuation. When the target depth is shallow, its refl ection echo signal will overlap with the background noise, affecting the detection of arrival time and localization of the target. Thus, we propose a noise attenuation method based on the curvelet transform. First, the original signal is transformed into the curvelet domain, and then the curvelet coefficients of the background noise are extracted according to the distribution features that differ from the effective signal. In the curvelet domain, the coarse-scale curvelet atom is isotropic. Hence, a two-dimensional directional filter is designed to estimate the high-energy background noise in the coarsescale domain, and then, attenuate the background noise and highlight the effective signal. In this process, we also use a subscale threshold value of the curvelet domain to fi lter out random noise. Finally, we compare the proposed method with the average elimination and 2D continuous wavelet transform methods. The results show that the proposed method not only removes the background noise but also eliminates the coherent interference and random noise. The numerical simulation and the real data application suggest and verify the feasibility and effectiveness of the proposed method.