Time-varying many-server finite-queues in tandem: Comparing blocking mechanisms via fluid models

This paper focuses on the mechanism of Blocking Before Service (BBS), in time-varying many-server queues in tandem. BBS arises in telecommunication networks, production lines and healthcare systems. We model a stochastic tandem network under BBS and develop its corresponding fluid limit, which includes reflection due to jobs lost. Comparing our fluid model against simulation shows that the model is accurate and effective. This gives rise to design/operational insights regarding network throughput, under both BBS and BAS (Blocking After Service).     

高波数问题的超收敛性

 本文考虑求解Helmholtz方程的有限元方法的超逼近性质以及基于PPR后处理方法的超收敛性质.我们首先给出了矩形网格上的p-次元在收敛条件k（kh）^2p+1≤C₀下的有限元解和基于Lobatto点的有限元插值之间的超逼近以及重构的有限元梯度和精确解之间的超收敛分析.然后我们给出了四边形网格上的线性有限元方法的分析.这些估计都给出了与波数k和网格尺寸h的依赖关系.同时我们回顾了三角形网格上的线性有限元的超收敛结果.最后我们给出了数值实验并且结合Richardson外推进一步减少了误差.     

A cyclic approach on classical ruin model

The ruin problem has long since received much attention in the literature. Under the classical compound Poisson risk model, elegant results have been obtained in the past few decades. We revisit the finite-time ruin probability by using the idea of cycle lemma, which was used in proving the ballot theorem. The finite-time result is then extended to infinite-time horizon by applying the weak law of large numbers. The cycle lemma also motivates us to study the claim instants retrospectively, and this idea can be used to reach the ladder height distribution on the infinite-time horizon. The new proofs in this paper link the classical finite-time and infinite-time ruin results, and give an intuitive way to understand the nature of ruin.     

Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling

We investigate a piecewise-deterministic Markov process with a Polish state space, whose deterministic behaviour between random jumps is governed by a finite number of semiflows. We provide tractable conditions ensuring a form of exponential ergodicity and the strong law of large numbers for the chain given by the post-jump locations. Further, we establish a one-to-one correspondence between invariant measures of the chain and those of the continuous-time process. These results enable us to derive the strong law of large numbers for the latter. The studied dynamical system is inspired by certain models of gene expression, which are also discussed here.     

社会网络环境下保护少数意见的风险性大群体应急决策方法

大群体决策过程中,少数意见十分重要,但考虑少数意见又有一定风险性,本文提出了一种社会网络环境下保护少数意见的风险性大群体应急决策方法。首先,利用自然语言处理技术对社交媒体中公众对突发事件的传播信息进行关键词提取,再采用TF-IDF技术提取公众关心的事件属性并确定属性权重;其次,将专家之间的联系考虑到决策当中,构建决策专家之间的社会网络关系;然后,建立少数意见的识别和风险测度机制,并定义了两个风险系数:信任风险系数和偏好风险系数,通过少数意见聚集的信任风险系数调节少数意见聚集的权重,通过偏好风险系数调节群体共识,以得到共识水平较高的大群体决策方案;最后,通过“7.1”宁乡洪灾案例分析,验证了所提方法的可行性和有效性。     

Existence of LSs

Let X be a ‐set and be a partition of X into n groups of size 2 and one group G₀ of size 4. A large‐set‐plus denoted by LS is a partition of all ‐transverse triples of X into block sets of 3‐GDD(2ⁿ4¹)s with group set , and two block sets of 3‐GDD(2ⁿ)s with group set . In this paper, we study the existence problem of LSs and give a nearly complete solution.     

Local Functional Limit Theorems of Increments for Brownian Motion

In this paper, we present a local Csrg–Révész type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Lévy's modulus of continuity for Brownian motion.     

Brown运动增量在H(o)lder范数下关于(r,p)-容度的泛函极限定理

利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理.     

可列齐次马氏链熵率的指数收敛速度

运用Markov不等式和期望、强遍历、δ系数的性质,利用Chang提出的研究指数收敛速度的方法,在给出5个引理的基础上,研究了初始状态给定的一类可列齐次马氏链熵率的收敛速度,推广了Chang的结果.