Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter （including p, q, r, λ, τ） on the mean first-passage time （MFPT） is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that （1） the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, （2） suppression appears on the curve of the MFPT with small λ （e.g. λ 〈 0.5） but there is a peak on the curve of the MFPT when λ is big （e.g. λ 〉 0.5）, and （3） with different values of r （e.g. r = 0.1, 0.5, 1.5）, the effort of τ on the MFPT is diverse.

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

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.

Mean First Passage Time for System with Fluctuating Potential Barrier and Coupled Noise

In this paper we study the mean first passage time （MFPT） over a fluctuation potential barrier driven by a coupled noise. It is shown that the MFPT over the fluctuation potential barrier displays resonant activations as the function of the flipping rate of the fluctuation potential barrier, and as the function of the dichotomous noise transition rate.

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 .

Distribution of First Passage Times for Lumped States in Markov Chains

First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis

Mean and variance of first passage time of non-homogeneous random walk

The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.

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.

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.

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.

Multi-Resonant-Activation for a System Only Driven by Multi-State Noise

We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.

Resonant Activation Induced by Four-Value Noise

The phenomenon of the resonant activation （RA） of a particle over a fluctuating potential barrier with a four-value noise is investigated. It is shown that the mean first passage time （MFPT） displays six minima as the function of the transition rates γ1, γ2, γ3, γ4, γ5, and 76 of the four-value noise, respectively. In addition, the effect of other parameters of the system, such as the noise strength D of the additive Gaussian white noise and the parameter value a, b, c, and d of the four-value noise, on the RAs is also investigated.

Biased Diffusive Search Triggered by ATP Binding During Kinesin's Stepping

In this paper, we present an asymmetry conformational potential with a reflecting boundary and an absorbing boundary, in which the diffusive search of the free head of kinesin motor can be biased toward its forward binding site. Under a wide range of condition, using first-passage time analysis we perform numerical simulation to the Langevin equation, and obtain the dependence of the dwell time for forward steps on the load force. And we calculate the expression for the dwell time by the Laplace transform method. Both numerical and analytical results show that the dwell times exponentially depend on the load force, which provide a simple physical explanation for experimental data. Our results suggest that ATP binding-conformation change in the neck linker plays an important role in unidirectional steps during kinesin＇s mechanochemical cycle.

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.

Study on the Recurrence Probability of Strong Earthquakes of Faults

Based on the physical model of Brownian passage time,the probabilities of recurrence of strong earthquakes on the major active faults in China are calculated in different predictive time spans,based mainly on the analysis of the earthquake preparation process before a strong earthquake occurs. Furthermore,the seismic risks on active faults are studied. The results show that the earthquake probabilities on the Xianshuihe fault,the Altyn Tagh fault,the east Kunlun fault and Xiaojiang fault are significantly greater than other faults in the Chinese mainland,which indicates that the level of stress accumulation on these faults are higher than on other faults. Therefore,these faults may have a seismic risk for strong earthquake in future.

A minimization problem of the risk probability in first passage semi-Markov decision processes with loss rates

This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.

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.

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.

Thermal preference, thermal tolerance and the thermal dependence of digestive performance in two Phrynocephalus lizards （Agamidae）, with a review of species studied

We reported data on thermal preference, thermal tolerance and the thermal dependence of digestive performance for two Phrynocephalus lizards （P. frontalis and P. versicolor）, and compared data among lizards so far studied worldwide. Mean values for selected body temperature （Tsel） and critical thermal maximum （CTMax） were greater in P versicolor, whereas mean values for critical thermal minimum （CTMin） did not differ between the two species. The two lizards differed in food intake, but not in food passage time, apparent digestive coefficient （ADC） and assimilation efficiency （AE）, across the experimental tem- peratures. Four general conclusions can be drawn from published data. Firstly, thermal preference and thermal tolerance differ among lizards differing in distribution, temporal activity pattern and habitat use. Lizards in thermally more variable regions are better able to tolerate low and high temperatures. Diurnal lizards generally select higher body temperatures than nocturnal lizards, and lizards using habitats with direct sun exposure generally selected higher body temperatures and are better able to tolerate high temperatures. Secondly, CTMax is positively correlated with Tsel. Lizards more likely exposed to extremely high temperatures while active select higher body temperatures than those using shaded habitats. Thirdly, the effects of body temperature on food intake, food passage time, ADC and AE differ among lizards, but it seems to be common among lizards that ADC and AE are less thermally sensitive than food intake and food passage time. Lastly, ADC is dependent on the type of food ingested, with insectivorous lizards digesting food more efficiently than herbivorous lizards