Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

大沙鼠的年龄鉴定

2002~2003年通过对精河甘家湖荒漠梭梭林国家级自然保护区大沙鼠的实地调查,共进行野外作业9次,设置100m×100m样方40个,采用样方面积夹子法,按5×20进行布夹,共布夹3964次,捕获大沙鼠(Rhomboms opimus)173只,其中雄94只,雌79只.通过对大沙鼠体重、体长、胴体重、胚胎及产仔情况、性腺发育状况的分析与比较,我们利用差异显著的胴体重为标准,将其划分为5个年龄组.其中雌鼠:1龄组幼体30~67g,2龄组亚成体62-85g,3龄组成体1组85~113g,4龄组成体2组113~147g,5龄组老体139~173g.雄鼠:1龄组幼体33~84g,2龄组亚成体61~102g,3龄组成体1组102~158g,4龄组成体2组113~153g,5龄组老体131~193g.     

具有急慢性阶段的SIS流行病模型的稳定性

本文系统研究了具有急性和慢性两个阶段的SIS流行病模型.由两节构成,第一节建立和研究了具有急性和慢性两个阶段的SIS流行病模型,该模型是由三个常微分方程构成的方程组;第二节在第一节的基础上建立和研究了具有慢性病病程的SIS流行病模型;该模型既含有常微分方程,又含有偏微分方程.假设所研究的国家或地区的总人口N(t)服从增长规律: N'(t)=A—μN(t),运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式．证明了无病平衡态的全局渐近稳定性,给出了两模型地方病平衡态的存在性和稳定性条件．     

Actuarial applications of the linear hazard transform in life contingencies

In this paper, we study the linear hazard transform and its applications in life contingencies. Under the linear hazard transform, the survival function of a risk is distorted, which provides a safety margin for pricing insurance products. Combining the assumption of α-power approximation with the linear hazard transform, the net single premium of a continuous life insurance policy can be approximated in terms of the net single premiums of discrete ones. Moreover, Macaulay duration, modified duration and dollar duration, all measuring the sensitivity of the price of a life insurance policy to force of mortality movements under the linear hazard transform, are defined and investigated. Some examples are given for illustration.     

CEO年龄、公司治理与海外并购——来自我国沪深股市的经验数据(2009~2014)

本研究基于高阶理论、委托代理理论和最优契约理论,运用沪深两市上市公司在2009~2014年的海外并购数据,对CEO年龄以及与CEO紧密相关的公司治理对企业海外并购决策进行了实证研究。实证结果表明:(1)CEO年龄整体上与企业海外并购决策负相关,说明年纪越大的CEO越不倾向于进行海外并购,越年轻的CEO则越倾向于实施海外并购。在年龄组Ⅰ(<=40岁)中,CEO年龄与企业海外并购决策在5%的水平上显著负相关,说明在年龄小于等于40岁的CEO中,也就是处于青年成熟期的CEO越倾向于实施海外并购;处于中年稳健期(年龄组Ⅲ,49~55岁)的CEO,随着管理经营经验的不断累积,年龄越大越倾向于实施海外并购。(2)在公司治理对海外并购决策的影响方面,股权集中度与海外并购决策正相关,股权集中程度越高就越容易进行海外并购;CEO持股比例与海外并购决策负相关,CEO持股比例越高,CEO越不会做出海外并购决策。     

Ultrasonic measurement of viscoelastic shear modulus development in hydrating cement paste

A test procedure for measuring changes in amplitude and phase of SH ultrasonic waves from the interface between fused-quartz and cement paste samples is presented. The phase change is determined from the temporal shift in the reflected signal relative to the incident signal. The sensitivity of the measured parameters to changes in acoustic impedance of the materials in contact with fused-quartz is evaluated for different angles of incidence. It is shown that a reflection measurement at normal incidence at nano-second temporal resolution does not provide sufficient sensitivity to measure the viscous component of shear modulus of low viscosity fluids and cannot be applied to cement paste while it is in a fluid state. Monitoring the measured amplitude and phase at oblique angle of incidence allows for measuring fluids with acoustic impedance comparable to cement paste. The reflection measurements are used to determine the evolution of elastic and viscous components of shear modulus cement paste with time. Influence of sampling rate and temperature effects on the phase measurements are evaluated and shown to be significant. It is shown that the initial loss of workability of cement paste through setting process is associated with a larger relative increase in the viscous component of shear modulus. Following the initial rapid rise of the viscous component of shear modulus, there is a larger relative increase in the elastic component, which can be related to the emergence of a solid structure capable of retaining an imprint.     

Strong convergence of the split‐step θ‐method for stochastic age‐dependent population equations

In this paper, we constructed the split‐step θ (SSθ)‐method for stochastic age‐dependent population equations. The main aim of this paper is to investigate the convergence of the SS θ‐method for stochastic age‐dependent population equations. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from the theory, and comparative analysis with Euler method is given, the results show the higher accuracy of the SS θ‐method. Copyright © 2014 John Wiley & Sons, Ltd.     

激光探针等离子体质谱测定单颗粒锆石铀-铅年龄

建立了一种利用激光探针等离子体质谱测定单颗粒锆石Ｕ－Ｐｂ同位素年龄的新方法。以线扫描进样法代替传统的剥深进样法,克服Ｕ／Ｐｂ之间的熔蚀分异。对前寒武纪锆石的定年表明,＾２０７Ｐｂ／＾２０６Ｐｂ／＾２３８Ｕ定年精密度和准确度均为优于２％。     

基于NBUMg类分布的更换策略比较

证明了年龄更换策略和成批更换策略依矩母函数序减少(增加)任意时间间隔内的失效次数的充要条件是基分布具有NBUMg (NWUMg)性质;更换间隔不同的成批更换策略在相同工作时间内的失效次数也作了比较.