Statistical evidence of strain induced breaking of metallic point contacts

As a paradigm for modeling gene regulatory networks, probabilistic Boolean networks (PBNs) form a subclass of Markov genetic regulatory networks. To date, many different stochastic optimal control approaches have been developed to find therapeutic intervention strategies for PBNs. A PBN is essentially a collection of constituent Boolean networks via a probability structure. Most of the existing works assume that the probability structure for Boolean networks selection is known. Such an assumption cannot be satisfied in practice since the presence of noise prevents the probability structure from being accurately determined. In this paper, we treat a case in which we lack the governing probability structure for Boolean network selection. Specifically, in the framework of PBNs, the theory of finite horizon Markov decision process is employed to find optimal constituent Boolean networks with respect to the defined objective functions. In order to illustrate the validity of our proposed approach, an example is also displayed.     

A semi-Markov model for price returns

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.     

First passage time and extremum properties of Markov and independent processes

It was shown by Newell in 1962 that the extreme value and first passage time distributions of various types of common Markov processes asymptotically approach those for independent random variables. In view of the great simplification this occasions in the calculation of a number of important properties of Markov processes, it is clearly of interest to determine in some detail the conditions on both the time and space variables under which this equivalence holds. In this paper we investigate and establish these conditions for Markov processes described by the Fokker-Planck equation and express them in simple analytic forms which are directly related to the coefficients of the Fokker-Planck equation. To demonstrate the usefulness of these conditions, we apply them to two representative examples of Fokker-Planck equations, the Ornstein-Uhlenbeck process and the Montroll-Shuler model for harmonic oscillator dissociation. It is shown very clearly in these examples that the extreme value and first passage time     

A singular perturbation approach to first passage times for Markov jump processes

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.     

Scheduling Strategy Design Framework for Cyber–Physical System with Non-Negligible Propagation Delay

Cyber–physical systems (CPS) have been widely employed as wireless control networks. There is a special type of CPS which is developed from the wireless networked control systems (WNCS). They usually include two communication links: Uplink transmission and downlink transmission. Those two links form a closed-loop. When such CPS are deployed for time-sensitive applications such as remote control, the uplink and downlink propagation delay are non-negligible. However, existing studies on CPS/WNCS usually ignore the propagation delay of the uplink and downlink channels. In order to achieve the best balance between uplink and downlink transmissions under such circumstances, we propose a heuristic framework to obtain the optimal scheduling strategy that can minimize the long-term average control cost. We model the optimization problem as a Markov decision process (MDP), and then give the sufficient conditions for the existence of the optimal scheduling strategy. We propose the semi-predictive framework to eliminate the impact of the coupling characteristic between the uplink and downlink data packets. Then we obtain the lookup table-based optimal offline strategy and the neural network-based suboptimal online strategy. Numerical simulation shows that the scheduling strategies obtained by this framework can bring significant performance improvements over the existing strategies.     

Mean first passage time of active Brownian particle in one dimension

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.     

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.     

Thermodynamic Formalism for Systems with Markov Dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism—a dynamical Gibbs ensemble construction—to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.     

First passage time problems for one-dimensional random walks

This note contains a development of the theory of first passage times for one-dimensional lattice random walks with steps to nearest neighbor only. The starting point is a recursion relation for the densities of first passage times from the set of lattice points. When these densities are unrestricted, the formalism allows us to discuss first passage times of continuous time random walks. When they are negative exponential densities we show that the resulting equation is the adjoint of the master equation. This is the lattice analog of a correspondence well known for systems describable by a Fokker-Planck equation. Finally we discuss first passage problems for persistent random walks in which at each step the random walker continues in the same direction as the preceding step with probability a or reverses direction with probability 1–     

Fractional nonlinear diffusion equation and first passage time

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with a space- and time-dependent diffusion coefficient subject to absorbing boundaries and the initial condition. We obtain explicit analytical expression for the probability distribution, the first passage time distribution, the mean first passage time, and the mean squared displacement corresponding to different time-dependent diffusion coefficient. In addition, we compare our results for the first passage time distribution and the mean first passage time with the one obtained by usual linear diffusion equation with time-dependent diffusion coefficient.     

A UoI-Optimal Policy for Timely Status Updates with Resource Constraint

Timely status updates are critical in remote control systems such as autonomous driving and the industrial Internet of Things, where timeliness requirements are usually context dependent. Accordingly, the Urgency of Information (UoI) has been proposed beyond the well-known Age of Information (AoI) by further including context-aware weights which indicate whether the monitored process is in an emergency. However, the optimal updating and scheduling strategies in terms of UoI remain open. In this paper, we propose a UoI-optimal updating policy for timely status information with resource constraint. We first formulate the problem in a constrained Markov decision process and prove that the UoI-optimal policy has a threshold structure. When the context-aware weights are known, we propose a numerical method based on linear programming. When the weights are unknown, we further design a reinforcement learning (RL)-based scheduling policy. The simulation reveals that the threshold of the UoI-optimal policy increases as the resource constraint tightens. In addition, the UoI-optimal policy outperforms the AoI-optimal policy in terms of average squared estimation error, and the proposed RL-based updating policy achieves a near-optimal performance without the advanced knowledge of the system model.     

Mixing search on complex networks

In this article, we derive the first passage time (FPT) distribution and the mean first passage time (MFPT) of random walks from multiple sources on networks. On the basis of analysis and simulation, we find that the MFPT drops substantially when particle number increases at the first stage, and converges to the shortest distance between the sources and the destination when particle number tends to infinite. Given the fact that a Brownian particle from a high-degree node often needs a large number of steps to reach an expected low-degree node, which is the bottleneck for a single random walk, we propose a mixing search model to improve the efficiency of search processes by using random walks from multiple sources to continue the searches from high-degree nodes to destinations. We compare our model with the mixing navigation model proposed by Zhou on complex networks and find that our model converges much faster with lower hardware cost than Zhou’s model. Moreover, simulations on scale-free networks show that the search efficiency of our model is much higher than that of a single random walk, and comparable to that of multiple random walks which have much higher hardware cost than our model. Finally, we discuss the traffic cost of our model, and propose an absorption strategy for our model to recover the additional walkers in networks. Simulations indicate that this strategy reduces the traffic cost of our model effectively.     

复杂高阶对象的预测PID控制

针对复杂高阶对象提出了一种基于数值最优模型降阶方法,并基于这种降阶模型设计了预测PID控制器,将此控制器应用于原始模型能够得到很好地控制效果。数值最优模型降阶算法使高阶对象能近似为一阶加时滞对象或二阶加时滞对象,通过模型阶跃响应和Bode图对比,降阶模型曲线很好地逼近原始模型曲线。预测PID对大时滞对象有着很好地控制效果,模型降阶使得预测PID很好地控制复杂高阶对象,且其结构简单,可调参数少的特点。     

Steady state speed distribution analysis for a combined cellular automaton traffic model

Cellular Automaton （CA） based traffic flow models have been extensively studied due to their effectiveness and simplicity in recent years. This paper develops a discrete time Markov chain （DTMC） analytical framework for a Nagel-Schreckenberg and Fukui Ishibashi combined CA model （W^2H traffic flow model） from microscopic point of view to capture the macroscopic steady state speed distributions. The inter-vehicle spacing Maxkov chain and the steady state speed Markov chain are proved to be irreducible and ergodic. The theoretical speed probability distributions depending on the traffic density and stochastic delay probability are in good accordance with numerical simulations. The derived fundamental diagram of the average speed from theoretical speed distributions is equivalent to the results in the previous work.     

Duality in Interacting Particle Systems and Boson Representation

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those with continuous state space. We clarify that using a generating function approach and the Doi-Peliti method, a birth-death process (or discrete random walk model) is naturally connected to a differential equation with continuous variables, which would be interpreted as a dual Markov process. The key point in the derivation is to use bosonic coherent states as a bra state, instead of a conventional projection state. As examples, we apply the scheme to a simple birth-coagulation process and a Brownian momentum process. The generator of the Brownian momentum process is written by elements of the SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same scheme is available.     

Moments of the First Passage Time Under External Driving

A general theory is derived for the moments of the first passage time of a one-dimensional Markov process in the presence of a weak time-dependent forcing. The linear corrections to the moments can be expressed by quadratures of the potential and of the time-dependent probability density of the unperturbed system or equivalently by its Laplace transform. If none of the latter functions is known, the derived formulas may still be useful for specific cases including a slow driving or a driving with power at only small or large times. In the second part of the paper, explicit expressions for the mean and variance of the first passage time are derived for the cases of a linear or a parabolic potential and an exponentially decaying driving force. The analytical results are found to be in excellent agreement with computer simulations of the respective first-passage processes. The particular examples furthermore demonstrate that already the effect of a simple exponential driving can be fairly involved implying a nontrivial nonmonotonic behavior of mean and variance as functions of the drivings time scale.     

Semi-Markov regime switching interest rate models and minimal entropy measure

In this paper, we present a discrete time regime switching binomial-like model of the term structure where the regime switches are governed by a discrete time semi-Markov process. We model the evolution of the prices of zero-coupon when given an initial term structure as in the model by Ho and Lee that we aim to extend. We discuss and derive conditions for the model to be arbitrage free and relate this to the notion of martingale measure. We explicitly show that due to the extra source of uncertainty coming from the underlying semi-Markov process, there are an infinite number of equivalent martingale measures. The notion of path independence is also studied in some detail, especially in the presence of regime switches. We deal with the market incompleteness by giving an explicit characterization of the minimal entropy martingale measure. We give an application to the pricing of a European bond option both in a Markov and semi-Markov framework. Finally, we draw some conclusions.     

A study on correlated exponential random walks

Based on the linear Boltzmann transport formulation, we investigate the statistics of correlated exponential random walks that are continuous in space and discrete in time. We show that asymptotically, the correlated random walk process is diffusive and derive an effective diffusion constant. We investigate the power spectral characteristics of the associated random forces. We also present some results on the first passage time distribution and establish that asymptotically it reduces to that associated with simple Gaussian walks.     

Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.     

色交叉关联噪声对基因转录调节系统的影响

研究了受色交叉关联噪声驱动的基因转录调节系统的瞬态性质(平均首通时间).据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,求出稳态概率分布函数的表达式.在此基础上运用最快下降法得到平均首通时间的近似表达式.经过数值计算,结果表明：在强关联,小关联时间条件下,蛋白质的浓度经历了开→关→开;在弱关联,大关联时间条件下,蛋白质的浓度经历了开→关.在基因转录过程中出现了重入现象. 关键词： 色交叉关联噪声 基因转录调节系统 平均首通时间