Noise Correlation Time Research Articles

Active transport improves the precision of linear long distance molecular signalling

Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices.

Signal power amplification of intracellular calcium dynamics with non-Gaussian noises and time delay

The effect of non-Gaussian noises on stochastic resonance of intracellular Ca2+ concentration in intracellular calcium oscillation(ICO) system with time delay is investigated by means of second-order stochastic Runge–Kutta type algorithm. By simulating the signal power amplification(SPA), the results indicate: there are respectively continuous values and a value of the parameter p(which is used to control the degree of the departure from the non-Gaussian noise and Gaussian noise.) to enhance reverse resonance in the behavior of SPA vs. p in cytosol and calcium store, namely continuous reverse resonance occurs in cytosol and reverse resonance occurs in calcium store. Moreover, SPA monotonically decreases as non-Gaussian noises strengthen, and SPA fast decays to constant as correlation time of non-Gaussian noises increases.

Statistics for anti-synchronization of intracellular calcium dynamics

The anti-synchronization of calcium oscillation between cytosol and calcium store in intracellular calcium oscillation system with non-Gaussian noises and time delay are studied by means of second-order stochastic Runge–Kutta type algorithm. Basic on statistic, the normalized global synchronization error of Ca2+ concentration in cytosol and calcium store is simulated, the results exhibit, it shifts into single trough from multi troughs structure as parameter p (which is used to control the degree of the departure from the non-Gaussian noise and Gaussian noise) or density of non-Gaussian noises increases, however, it shifts into multi troughs from single trough structure as correlation time of non-Gaussian noises increases. In addition, the short, moderate, and long time delay respectively induce anti-synchronously quasi-periodic, synchronously quasi-periodic, and chaotic oscillation.

Demonstration of a quantum error correction for enhanced sensitivity of photonic measurements

The sensitivity of classical and quantum sensing is impaired in a noisy environment. Thus, one of the main challenges facing sensing protocols is to reduce the noise while preserving the signal. State of the art quantum sensing protocols that rely on dynamical decoupling achieve this goal under the restriction of long noise correlation times. We implement a proof-of-principle experiment of a protocol to recover sensitivity by using an error correction for photonic systems that does not have this restriction. The protocol uses a protected entangled qubit to correct a single error. Our results show a recovery of about 87% of the sensitivity, independent of the noise rate.

Stability of a Beddington–DeAngelis type predator–prey model with trichotomous noises

The stability analysis of a Beddington–DeAngelis (B–D) type predator–prey model driven by symmetric trichotomous noises is presented in this paper. Using the Shapiro–Loginov formula, the first-order and second-order solution moments of the system are obtained. The moment stability conditions of the B–D predator–prey model are given by using Routh–Hurwitz criterion. It is found that the stabilities of the first-order and second-order solution moments depend on the noise intensities and correlation time of noise. The first-order and second-order moments are stable when the correlation time of noise is increased. That is, the trichotomous noise plays a constructive role in stabilizing the solution moment with regard to Gaussian white noise. Finally, some numerical results are performed to support the theoretical analyses.

Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

In this paper, the transition between the stable state of a big density and the extinction state and stochastic resonance (SR) for a time-delayed metapopulation system disturbed by colored cross-correlated noises are investigated. By applying the fast descent method, the small time-delay approximation and McNamara and Wiesenfeld’s SR theory, we investigate the impacts of time-delay, the multiplicative, additive noises and colored cross-correlated noise on the SNR and the shift between the two states of the system. Numerical results show that the multiplicative, additive noises and time-delay can all speed up the transition from the stable state to the extinction state, while the correlation noise and its correlation time can slow down the extinction process of the population system. With respect to SNR, the multiplicative noise always weakens the SR effect, while noise correlation time plays a dual role in motivating the SR phenomenon. Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon. Conversely, it could motivate the SR effect to increase the strength of the cross-correlation noise in the SNR-β plot, while the increase of additive noise intensity will firstly excite SR, and then suppress the SR effect.

The mean first passage time and stochastic resonance in gene transcriptional system with time delay

In this paper, the gene transcriptional dynamics driven by correlated noises are investigated, where the time delay for the synthesis of transcriptional factor is introduced. The effects of the noise correlation strength and time delay on the stationary probability distribution (SPD), the mean first passage time and the stochastic resonance (SR) are analyzed in detail based on the delay Fokker–Planck equation. It is found that both the time delay and noise correlation strength play important roles in the bistable transcriptional system. The effect of the correlation strength reduces but the time delay enhances the mean first passage time (MFPT). Finally, the SR for this gene transcriptional system is found to be enhanced by the time delay.

Mean extinction time and stability for a metapopulation system subjected to correlated Gaussian and non-Gaussian noises

In this paper, we investigate the shift between the stable state of a large density and the extinction state, the mean extinction time for a metapopulation system induced by the associated Gaussian additive noise and non-Gaussian multiplicative noise. By applying the approximate Fokker–Planck equation, the fast descent method and the path integral approach, we obtain the expressions of the effective potential function and the mean extinction time. The numerical results show that the additive noise can damage the stability of the system, while the associated noise and the noise correlation times τ0 and τ can strengthen the stability of the population system. In the meantime, the maximum of the mean first-passage time appears in the meta-population system due to the impacts of different types of noises and their correlation time terms. It can effectively extend the extinction time of the metapopulation to enhance the strength of the correlation noise and two terms of noise correlation time. Conversely, the additive noise plays a negative role in preventing the extinction of the population. On the other side, a proper small multiplicative noise intensity can produce the positive effect on lengthening the life of the metapopulation.

Chain reconfiguration in active noise

In a typical single molecule experiment, the dynamics of an unfolded protein is studied by determining the reconfiguration time using long-range Förster resonance energy transfer, where the reconfiguration time is the characteristic decay time of the position correlation between two residues of the protein. In this paper we theoretically calculate the reconfiguration time for a single flexible polymer in the presence of active noise. The study suggests that though the mean square displacement grows faster, the chain reconfiguration is always slower in the presence of long-lived active noise with exponential temporal correlation. Similar behavior is observed for a worm-like semi-flexible chain and a Zimm chain. However it is primarily the characteristic correlation time of the active noise and not the strength that controls the increase in the reconfiguration time. In brief, such active noise makes the polymer move faster but the correlation loss between the monomers becomes slow.

Velocity distribution in active particles systems.

We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions. Our model shows that, even for two particles only, the individual velocities display a variance depending on the interparticle separation and the emergence of correlations between the velocities of the particles. When considering systems composed of many particles we find an analytic expression connecting the overall velocity variance to density, at the mean-field level, and to the pair distribution function valid in the limit of small noise correlation times. Finally we discuss the intriguing analogies and main differences between our effective free energy functional and the theoretical scenario proposed so far for phase-separating active particles.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

TUMOR CELL GROWTH SUBJECTED TO CORRELATED NOISES AND TIME DELAY

The tumor cell growth with time-delayed feedback driven by correlated noises under the immune surveillance are investigated within an anti-tumor model. The effects of the noise correlation strength and time delay on the stationary probability distribution, the average tumor cell population and the mean first passage time (MFPT) are analyzed in detail based on the delay Fokker–Planck equation. The effects of the correlation strength and time delay could play the same role in the average tumor cell population, but play opposite role in the MFPT. In addition, the role of the correlation strength and time delay for different activation thresholds of immune system is explored.

Steady state characteristics in FHN neural system driven by correlated non-Gaussian noise and Gaussian noise

Recently, the dynamics problems of nonlinear systems driven by noises have attracted considerable attention. The researches indicate that the noise plays a determinative role in system evolution. This irregular random interference does not always play a negative role in the macro order. Sometimes it can play a positive role. The various effects of noise are found in physics, biology, chemistry and other fields, such as noise-induced non-equilibrium phase transition, noise-enhanced system stability, stochastic resonance, etc. Especially, in the field of biology, the effects of noise on life process are significant. At present, a large number of researchers have studied the kinetic properties of the neuron system subjected to noises. However, these studies focus on the Gaussian noise, while the researches about non-Gaussian noise are less. In fact, it is found that all the noise sources among neuronal systems, physical systems and biological systems tend to non-Gaussian distribution. So it is reasonable to consider the effects of the non-Gaussian noise on systems, and it is closer to the actual process. Therefore, it has some practical significance to study the FHN system driven by the non-Gaussian noise and analyze the kinetic properties of this system. In this work, we study the stationary probability distribution (SPD) in FitzHugh-Nagumo (FHN) neural system driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and the unified colored approximation, the analytical expression of the stationary probability distribution is first derived, and then the change regulations of the SPD with the strength and relevance between multiplicative noise and additive noise are analyzed. After that, the simulation results show that the intensity of multiplicative noise, the intensity of additive noise, the correlation time of the non-Gaussian noise and the cross-correlation strength between noises can induce non-equilibrium phase transition. This means that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. However, the non-Gaussian noise deviation parameter cannot induce non-equilibrium phase transition. Moreover, we also find that the increases of the multiplicative noise intensity and the cross-correlation strength between noises are conducive to the conversion of the exciting state into the resting state. And with the additive noise intensity and the correlation time increasing, the conversion of the resting state into the exciting state becomes obvious. Meanwhile, the increase of non-Gaussian noise deviation parameter increases the probability of staying in the resting state.

Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations

In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias current. As a first step, the analysis is carried out in the presence of an external Gaussian white noise source, which mimics the random fluctuations of the bias current. Varying the noise intensity, it is possible to analyze the behavior of the escape time from a superconductive metastable state in different temperature regimes. Noise induced phenomena, such as resonant activation and noise induced stability, are observed. The study is extended to the case of a coloured Gaussian noise source, analyzing how the escape time from the metastable state is affected by correlated random fluctuations for different values of the noise correlation time.

Effect of a noisy driving field on a bistable polariton system

We report on the effect of noise on the characteristics of the bistable polariton emission system. The present experiment provides a time-resolved access to the polariton emission intensity. We evidence the noise-induced transitions between the two stable states of the bistable polaritons. It is shown that the external noise specifications, intensity and correlation time, can efficiently modify the polariton Kramers time and residence time. We find that there is a threshold noise strength that provokes the collapse of the hysteresis loop. The experimental results are reproduced by numerical simulations using Gross-Pitaevskii equation driven by a stochastic excitation.

Stochastic bifurcations induced by correlated noise in a birhythmic van der Pol system

We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker–Planck equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.

Characterization of integrated noises driving bacterial degradation kinetics in the water environment by Fourier transform algorithm

Integrated noises are used in this study for tackling uncertainties in the dynamic energy budget model (DEB) to study bacterial degradation kinetics in water environment. According to the Fourier transform algorithm, the R2 coefficients in the regression equation are greater than 0.9 and more than 80 % of the data are close to true ones, indicating that the transform algorithm is satisfactory in identifying intensity (B) and correlation time (τ) of noises existing in the DEB model. The major findings include: (1) bacterial cells are not suitable for survival under certain integrated-noises scenarios (intensity B is more than 10−2 or constant time τ is greater than 100); (2) the conversion value is closer to the true value when the estimate sample is greater; (3) a well-identified running number (around 400 times in this study) is helpful in improving the estimation accuracy; (4) the larger the true values of B and τ, the lower the estimation accuracy. In addition, more efforts are still desired for noises characterization, for example, the reorganization of integrated noises and correlation among noises.

Simulating Study of the Effects of the Color Pump Noise on the Two-mode Laser System

The color pump noise has been introduced into a two-mode laser system and its effects on the laser system in both homogeneously and inhomogeneously broadened media have been studied. The results show that the correlation time of the color pump noise can make the distribution of the laser intensity concentrate in the region where the laser intensity have larger values, enhance the mean of the laser intensity and stabilize the the system in a homogeneously broadened two-mode laser system; meanwhile, it strengthen the laser intensity of the stronger mode, recedes the laser intensity of the weaker mode and increases the competition between two mode in a inhomogeneously broadened two-mode laser system. Comparatively, it more clear that the influences of the color pump noise on the statistical properties of laser system in inhomogeneously broadened media than that in homogeneously broadened media.

Ghost responses of the FitzHugh–Nagumo system induced by colored noise

We investigate both numerically and experimentally how the triggering of Ghost Stochastic Resonance is affected by colored noise in a FitzHugh–Nagumo circuit. It is experimentally shown that when the circuit is excited with a bichromatic signal, weak colored noise can induce a response with a main ghost frequency which is not present in the excitation. We analyze the occurrence of this ghost frequency versus the noise intensity and the correlation time of the colored noise. Numerical simulations and experiments confirm that for larger noise correlation time, submultiples of this ghost frequency dominate the system response while the previous expected ghost frequency is less observed.