A Note of the Uniqueness Criterion for Single Birth Processes

This paper is devoted to studying the si ngle birth processes. The uniqueness criterion for the processes is presented.

Unified representation of formulas for single birth processes

Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.

SINGLE BIRTH PROCESSES

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes

We obtain sufficient criteria for central limit theorems （CLTs） for ergodic continuous-time Markov chains （CTMCs）. We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we present an explicit expression of the time average variance constant for a single birth process whenever a CLT exists. Several examples are given to illustrate these results.

On Variation of Single Birth Processes

Suppose {X（t）; t≥ 0} is a single birth process with birth rate qii＋l （i 〉 0） and death rate qij （i 〉 j ≥ 0）. It is proved in this paper that （i） if there exists aconstant c≥ 0 such that b（i）-a（i）＋ci is nondecreasing with respect to i and a（i） ＋ u（i） - ci ≥ 0 （i≥ 0）, then VarX（t）-EX（t）≥-X（0）e^-2ct,t≥0,or （ii） if there exists a constant u（i） - c≥ 0 such that b（i）-a（i）＋ci is non-increasing with respect to i and a（i）＋u（i）-ci≤0（i≥0）,then VarX（t） - EX（t） ≤ -X（0）e^-2c,t ≥ 0 Hereb（i） = qii＋1, a（0） = 0, a（i） = ∑j=^ijqii-j （i≥ 1）, u（0） = u（1） =0 and u（i） = 1/2∑j=^ij（j - 1）qii-j （i ≥ 2） . This result covers the results for birth-death processes obtained in [7].

THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.

A General Repairable Spare Part Demand Model Based on Quasi Birth and Death Process

This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.

The Wartime Bridge Reliability Evaluation Model Based on Birth-and-Death Process

At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network, the state diversion process is proved to be birth-and-death process. In the end, the state diversion balance equation of bridge network is built, and the evaluation model of wartime bridge reliability is got. The model is used in a certain example, and it is proved to be precise and credible.

Finite family trees of continuous time birth and death processes for evaluating the transmitting speed of information on communication networks

A finite random graph generated by continuous time birth and death processes with exponentially distributed waiting times was investigated, which is similar to a communication network in daily life. The vertices are the living particles, and directed edges go from mothers to daughters. The size of the communication network was studied. Furthermore, the probability of successfully connecting senders with receivers and the transmitting speed of information were obtained.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

Logarithmic Sobolev Inequalities for Two-Sided Birth-Death Processes

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for a is also presented.

Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2 × 2 games in a well-mixed population with a finite size is investigated. In the model, the individuals＇ payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength β and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when s is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the ＇Hawk-Dove＇ game and the ＇Coordinate＇ game are used to illustrate our model. We give the evolutionary stable strategy （ESS） of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.

The entanglement of two moving atoms interacting with a single-mode field via a three-photon process

In this paper, the entanglement of two moving atoms induced by a single-mode field via a three-photon process is investigated. It is shown that the entanglement is dependent on the category of the field, the average photon number N, the number p of half-wave lengths of the field mode and the atomic initial state. Also, the sudden death and the sudden birth of the entanglement are detected in this model and the results show that the existence of the sudden death and the sudden birth depends on the parameter and the category of the mode field. In addition, the three-photon process is a higher order nonlinear process.

A Linear Immigration-Birth-Death Model and Its Statistical Inference

formula of simulation proccss by In this paper, we employ monmnt generating function to obtain some exact transition probability of inlmigration-birth-death（IBD） model and discuss the of sample path and statistical inference with complete observations of the IBD the exact transition density formula.

The First- Passage Time Moment of the GNP Diffusion Process to a Determined Value

This paper describes an accurate method of approximating the moments of the first-passage time for the birth and death Gross National Product GNP diffusion process when the GNP is a determined value or constant absorbing barrier. This was done by approximating the differential equations by equivalent difference equations.

Inferring Multi-Type Birth-Death Parameters for a Structured Host Population with Application to HIV Epidemic in Africa

Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.

一类二次矩阵方程的牛顿迭代法及其收敛性

二次矩阵方程是科学与工程计算中一类重要的方程,探讨有效的数值方法是一项有意义的工作,拟生灭过程在股价模拟、库存控制、排队论等很多领域都有着重要的应用,对一类来源于拟生灭过程的特殊的二次矩阵方程进行了研究。在最小非负解存在且唯一的假设条件下,提出了牛顿迭代法并证明其收敛性。当初始矩阵取零矩阵时,牛顿迭代法产生的矩阵列收敛到方程的唯一最小非负解。最后通过数值例子验证算法的有效性与可行性。

基于飞机状态的备件动态规划技术

伴随民航业的竞争日趋激烈,航空公司迫切需要控制成本以提升效益。民机备件既是直接影响飞行安全的关键因素,备件成本又在航空公司可控成本中占比最高。因此,在保证飞行安全的前提下做好备件规划,对航空公司有至关重要的意义。根据民机备件的安全级别、故障修复时限等对备件分级设置保障率水平,采用符合备件故障特性的马尔可夫生灭过程,建立满足给定保障率水平的备件量计算模型,并在此基础上建立以保障成本最低为目标函数,满足保障率水平为约束函数的备件量动态规划模型。基于飞机状态分析历史故障数据、季节性、日利用率、机队规模对备件保障的影响,在所建模型中将故障率季节性差异、日利用率和飞机停场损失淡旺季差异进行评估以减小计算结果与实际需求的偏差。以H航空公司ERJ-190机型显示组件为例,对所建模型进行应用验证,计算结果与H航空公司运营实际相吻合,证明所建模型可为航空公司备件规划提供技术方法支持。

分娩镇痛初产妇产程中入量管理研究

目的 探讨饮食方式对分娩镇痛足月初产妇分娩结局的影响。方法 单胎足月初产妇400例随机分为观察组和对照组,观察组行入量管理及个体化的饮食指导。对照组根据孕妇的意愿进食水,比较2组分娩质量,初产妇呕吐,发生率、因宫缩乏力使用缩宫素率、产时发热率、会阴侧切率、转剖宫产率、阴道助产率、产后出血率;比较2组第一产程时间、第二产程时间、分娩镇痛时长及产后2 h出血量;比较2组新生儿Apgar评分、随机血糖、脐动脉血pH值、脐动脉血乳酸(Lac)值、新生儿窒息发生率、新生儿发热率、新生儿血糖异常发生率。结果 观察组产妇呕吐的发生率、因宫缩乏力使用缩宫素率、产时发热率、会阴侧切率、转剖宫产率、阴道助产率均低于对照组;观察组产后出血率、第一产程时间、第二产程时间、分娩镇痛时长及产后2 h出血量小于对照组,观察组新生儿高血糖的发生率和新生儿低血糖发生率低于对照组,差异均有统计学意义(P<0.05)。2组脐动脉血pH值、Lac值、新生儿Apgar评分、新生儿随机血糖、新生儿窒息率、新生儿发热率比较,差异无统计学意义(P>0.05)。结论 产程中对产妇进行入量管理及个体化的饮食指导可以减少宫缩乏力发生率,缩短产程持续时间,降低难产发生率,减少产后2 h出血量及降低新生儿血糖异常的发生率。

基于任务生灭过程模型的边缘计算批处理调度算法分析与设计

移动边缘计算技术为低时延要求、资源敏感的计算任务需求提供解决方案,通过研究任务请求特征以提高调度算法效率是边缘计算的重要研究方向。不同于现有研究将任务请求特征建模为单一随机变量的做法,提出基于任务请求生灭过程模型的边缘计算架构,将求解最优调度决策的过程建模为无限期平均成本马尔可夫决策过程。在使用贝尔曼方程分析问题的过程中,利用任务的生灭特性对未来的请求到达做出估计以判断当前决策对未来系统时延能耗成本的影响,进而辅助确定当前状态的最优决策,并结合任务相关性感知提出批处理任务调度控制算法。所提算法根据生灭状态信息对策略迭代的状态空间和决策空间进行剪枝以降低策略改进的复杂度,突破了策略迭代算法的复杂度瓶颈。仿真结果表明,所提算法相较于传统的策略迭代算法具有明显的低复杂度优势,且能在不同系统条件下保持低时延、能耗成本。