The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour

The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .

Logical stochastic resonance in a cross-bifurcation non-smooth system

This paper investigates logical stochastic resonance(LSR)in a cross-bifurcation non-smooth system driven by Gaussian colored noise.In this system,a bifurcation parameter triggers a transition between monostability,bistability and tristability.By using Novikov's theorem and the unified colored noise approximation method,the approximate Fokker-Planck equation is obtained.Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations.We simulate the logic operation of the system in the bistable and tristable regions respectively.We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter.Furthermore,it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region,since the tristable region is more sensitive to noise than the bistable one.

Could one single dichotomous noise cause resonant activation for exit time over potential barrier?

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.

First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs

This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal （or ε-optimal） stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.

First Passage Risk Probability Minimization for Piecewise Deterministic Markov Decision Processes

This paper is an attempt to study the minimization problem of the risk probability of piecewise deterministic Markov decision processes(PDMDPs)with unbounded transition rates and Borel spaces.Different from the expected discounted and average criteria in the existing literature,we consider the risk probability that the total rewards produced by a system do not exceed a prescribed goal during a first passage time to some target set,and aim to find a policy that minimizes the risk probability over the class of all history-dependent policies.Under suitable conditions,we derive the optimality equation(OE)for the probability criterion,prove that the value function of the minimization problem is the unique solution to the OE,and establish the existence ofε(≥0)-optimal policies.Finally,we provide two examples to illustrate our results.

Quantum intelligence on protein folding pathways

We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues.We introduce the concept of distance space and its projections on a XY-plane,and two characteristic quantities,one is called compactness of protein structure and another is called probability ratio involving shortest path.The concept of shortest path enables us to reduce the 388×388 density matrix to a 2×2 one from which the von Neumann entropy reflecting certain quantum coherence feature is naturally defined.We observe the time evolution of average distance and compactness solved from the classical random walk and quantum walk,we also compare the features of the time-dependence of Shannon entropy and von Neumann entropy.All the results not only reveal the fast quantum folding time but also unveil the existence of quantum intelligence hidden behind in choosing protein folding pathways.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

Spherical Confinement Generates Entropic Force to Accelerate Polymer Chain Detachment

To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape of a Brownian particle from the potential well of the spring. However, as the free dangling length of the polymer chain increases, the conformational entropy of the chain is affected by geometric confinement. It means that the wall exerts a repulsive force on the chain, resulting in accelerated link detachment from a macroscopic perspective. In this work, we investigate the effect of entropy on the detachment rate in the case where the substrate is spherical. We demonstrate that spherical confinement accelerates chain detachment both inside and outside the sphere. An analytical expression for the mean detachment time of breakable links is given, which includes an additional pre-factor that is related to the partition function. Additionally, we analyze the expressions for entropic forces inside the sphere, outside the sphere, and on a flat wall, comparing their magnitudes to explain the difference in mean detachment time.

Slowing down critical transitions via Gaussian white noise and periodic force

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real systems.The residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.

Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.