Drift Analysis in Studying the Convergence and Hitting Times of Evolutionary Algorithms: An Overview

This paper introduces drift analysis approach in studying the convergence and hitting times of evolutionary algorithms. First the methodology of drift analysis is introduced, which links evolutionary algorithms with Markov chains or supermartingales. Then the drift conditions which guarantee the convergence of evolutionary algorithms are described. And next the drift conditions which are used to estimate the hitting times of evolutionary algorithms are presented. Finally an example is given to show how to analyse hitting times of EAs by drift analysis approach.

Weak Horseshoe with Bounded-Gap-Hitting Times

In this paper,we consider weak horseshoe with bounded-gap-hitting times.For a flow(M,Ф),it is shown that if the time one map(M,Ф_(1))has weak horseshoe with boundedgap-hitting times,so is(M,Ф_(τ))for all τ≠0.In addition,we prove that for an affine homeomorphism of a compact metric abelian group,positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.

双圈图中Hitting Time的极值问题

设HG(x,y)是图G上的随机游走中,从顶点x到顶点y的步数的期望值。本文主要研究一类双圈图G中φ(G)的极值问题,其中φ(G)=max{HG(x,y):x,y∈V(G)}。利用有效电阻,刻画出了在这类双圈图中,φ(G)达到极值时,相应的极图以及两点在图中的位置。

The Joint Distribution of the Maximum Excursion and the Minimum Excursion for Brownian Motion with Drift

In this paper, we discuss the problem of extreme value for Brownian motion with positive drift. We obtain the joint distribution of the maximum excursion and the minimum excursion.

HITTING TIME AND PLACE TO A SPHERE OR SPHERICAL SHELL FOR BROWNIAN MOTION

In this paper, the authors compute the explicit formulas for the joint distributions of thehitting time and place for a sphere or concentric spherical shell by Brownian motion, when theprocess starts either outside the sphere or the region bounded by concentric spheres.

Criteria on ergodicity and strong ergodicity of single death processes

Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.

A new remaining useful life estimation method for equipment subjected to intervention of imperfect maintenance activities

As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.

Muon tracking with the fastest light in the JUNO central detector

Background:The Jiangmen Underground Neutrino Observatory(JUNO)is a multi-purpose neutrino experiment designed to measure the neutrino mass hierarchy using a central detector(CD),which contains 20 kton liquid scintillator(LS)surrounded by about 18,000 photomultiplier tubes(PMTs),located 700 m underground.Purpose:The rate of cosmic muons reaching the JUNO detector is about 3 Hz,and the muon-induced neutrons and isotopes are major backgrounds for the neutrino detection.Reconstruction of the muon trajectory in the detector is crucial for the study and rejection of those backgrounds.Methods:This paper will introduce the muon-tracking algorithm in the JUNO CD,with a least-squares method of PMTs’first-hit time(FHT).Correction of the FHT for each PMT was found to be important to reduce the reconstruction bias.Results:The spatial resolution and angular resolution are better than 3 cm and 0.4 degree,respectively,and the tracking efficiency is greater than 90%up to 16 m far from the detector center.

Controller area network node reliability assessment based on observable node information

Controller area network(CAN) based fieldbus technologies have been widely used in networked manufacturing systems. As the information channel of the system, the reliability of the network is crucial to the system throughput, product quality, and work crew safety. However, due to the inaccessibility of the nodes' internal states, direct assessment of the reliability of CAN nodes using the nodes' internal error counters is infeasible. In this paper, a novel CAN node reliability assessment method, which uses node's time to bus-off as the reliability measure, is proposed. The method estimates the transmit error counter(TEC) of any node in the network based on the network error log and the information provided by the observable nodes whose error counters are accessible.First, a node TEC estimation model is established based on segmented Markov chains. It considers the sparseness of the distribution of the CAN network errors. Second, by learning the differences between the model estimates and the actual values from the observable node, a Bayesian network is developed for the estimation updating mechanism of the observable nodes. Then, this estimation updating mechanism is transferred to general CAN nodes with no TEC value accessibility to update the TEC estimation. Finally, a node reliability assessment method is developed to predict the time to reach bus-off state of the nodes. Case studies are carried out to demonstrate the effectiveness of the proposed methodology. Experimental results show that the estimates using the proposed model agree well with actual observations.

Explicit criteria on separation cutoff for birth and death chains

The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.

Random coverings of the circle with i.i.d.centers

Consider the random intervals In（W） ：= （wn -en/2,Wn ＋en/2）（mod 1） with their centers wn being i.i.d, but not necessary uniformly distributed on the circle T = R/Z and with their lengths decreasing to zero. Using the dimension theory in dynamical systems, we give conditions on which the circle is finitely or infinitely often covered by intervals {In （ w ） } n≥ 1.

The Birth–death Processes with Regular Boundary: Stationarity and Quasi-stationarity

For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.

STATISTICS OF A CLASS OF MARKOV CHAINS

In this paper we prove that the distributions of their sojourn time and hitting time at one special state for random walks which are allowed to be finite or infinite and Markov chains on star-graphs with discrete time can uniquely determine the probability distribution of the whole chains. This result also suggests a new statistical method for Markov chains.

THE RANGE OF RANDOM WALK ON TREES AND RELATED TRAPPING PROBLEM

This paper treats of the range of the simple random walk on trees and a related trapping problem. The strong law of large numbers and the central limit theorem for the range, and some asymptotic behaviour for the mean trapping time and survival probability are presented.