Response-adaptive trial designs with accelerated Thompson sampling

In a clinical trial, sometimes it is desirable to allocate as many patients as possible to the best treatment, in particular, when a trial for a rare disease may contain a considerable portion of the whole target population. The Gittins index rule is a powerful tool for sequentially allocating patients to the best treatment based on the responses of patients already treated. However, its application in clinical trials is limited due to technical complexity and lack of randomness. Thompson sampling is an appealing approach, since it makes a compromise between optimal treatment allocation and randomness with some desirable optimal properties in the machine learning context. However, in clinical trial settings, multiple simulation studies have shown disappointing results with Thompson samplers. We consider how to improve short-run performance of Thompson sampling and propose a novel acceleration approach. This approach can also be applied to situations when patients can only be allocated by batch and is very easy to implement without using complex algorithms. A simulation study showed that this approach could improve the performance of Thompson sampling in terms of average total response rate. An application to a redesign of a preference trial to maximize patient's satisfaction is also presented.     

文化空缺视阈下的英汉数字内涵对比研究

从空缺理论的角度，分析形成文化空缺的根源，并从完全空缺、冲突空缺、部分空缺和零空缺四个方面对英汉数字的文 化内涵进行比较研究。每个承载着强烈文化信息的数字在不同文化中都是独一无二的，对数字文化蕴涵的异同性的探究加深 了对英汉文化的理解，有助于感知文化的多样性和差异性，消除跨文化交际中的误解，促进中西方文化交流。     

基于样本集的区间数灰靶分类决策模型及应用

基于灰靶思想的不确定背景分类决策问题分析,本文提出了区间数灰靶分类决策模型。该模型将灰靶决策拓展到决策信息为区间数的情况,提出了区间数的靶心距测度方法;根据靶心距提出了灰靶分类决策中的靶心分类临界值设置方法;以决策对象的靶心距与临界值之间的偏差总量最小为目标,建立了指标权重和分类临界值的确定模型;依据求解的权重与分类临界值对决策对象集进行分类评价。算例分析验证了该模型的有效性和可行性,可以很好地解决决策对象众多、分类数不确定等特性的多属性分类决策问题。     

Does Market Incompleteness Matter?

This paper argues that incompleteness of intertemporal financial markets has little effect (on welfare, prices, or consumption) in an economy with a single consumption good, provided that traders are long–lived and patient, a riskless bond is traded, shocks are transitory, and there is no aggregate risk. In an economy with aggregate risk, a similar conclusion holds, provided traders share the same CRRA utility function and the right assets are traded. Examples demonstrate that these conclusions need not hold if the wrong assets are traded or if the economy has multiple consumption goods.     

On three and four vicious walkers

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of configurations of three vicious walkers to the enumeration of configurations of two vicious walkers. More precisely, the reflection principle leads to a bijection between three walks (L₁, L₂, L₃) such that L₂ intersects both L₁ and L₃ and three walks (L₁, L₂, L₃) such that L₁ intersects L₃. Hence we find a combinatorial interpretation of the formula for the generating function for the number of configurations of three vicious walkers, originally derived by Bousquet-Mélou by using the kernel method, and independently by Gessel by using tableaux and symmetric functions. This answers a question posed by Gessel and Bousquet-Mélou. We also find a reflection principle for four vicious walks that leads to a combinatorial interpretation of a formula derived from Gessel's theorem.     

Counting strings at height j in Dyck paths

Let τ be an arbitrary lattice path, called in this context string, consisting of two kinds of steps (rises and falls) and let j be a non-negative integer.In this paper, the explicit formula for the generating function F_j associated with the Dyck path statistic “number of occurrences of τ at height j” is evaluated.For the expression of F_j some basic characteristics of the string are used, namely its number of rises, height, depth and periodicity, as well as the generating function of the Catalan numbers.     

A new generation of process capability indices based on fuzzy measurements

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCI C_p compares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI, C_pm incorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices.     

Strong Law of Large Numbers for Countable Asymptotic Circular Markov Chains

In this article, we introduce the notion of a countable asymptotic circular Markov chain, and prove a strong law of large numbers: as a corollary, we generalize a well-known version of the strong law of large numbers for nonhomogeneous Markov chains, and prove the Shannon-McMillan-Breiman theorem in this context, extending the result for the finite case.     

分流墙的设置对疏散效率和安全性影响的研究

基于元胞自动机建立了地板场模型并进行赋值,通过考虑行人到出口的距离和出口前的人群密度提出了合理的出口选择模型,并引入了冲突函数来解决逃生者之间冲突的问题。以出口流率和冲突次数作为两个指标来分析分流墙对疏散效率及疏散安全性的影响规律。通过大量的疏散仿真实验对分流墙的长度及分流墙到出口的距离对疏散效率的影响进行研究,发现一定长度的分流墙能够明显降低冲突的次数,提高疏散的安全性;而分流墙到出口的距离合理设置能够提高疏散效率。