Bi-Objective Median Subtree Location Problems

A number of network design problems can be built on the following premise: given an undirected tree network, T, with node set, V, identify a single subtree, t, containing nodes, v, so that the subtree is located optimally with respect to the remaining, subset of unconnected nodes {V–v}. Distances between unconnected nodes and nodes in the subtree t can be defined on paths that are restricted to lie in the larger tree T (the restricted case), or can be defined on paths in an auxiliary complete graph G (the unrestricted case). The unrestricted case represents a class of problems that is not explicitly recognized in the literature, which is of intermediate complexity relative to the widely studied restricted case, and the general problem in which the underlying graph is general. This paper presents the Median Subtree Location Problem (MSLP), formulated as a bicriterion problem that trades off the cost of a subtree, t, against the population-weighted travel distance from the unconnected nodes to nodes on the subtree where both objectives are to be minimized. Integer programs were formulated for the travel restricted and travel unrestricted cases and were tested using linear programming and branch and bound to resolve fractions. Tradeoff curves between cost and travel burden were developed for sample networks.     

Admissibility of unbiased tests for a composite hypothesis with a restricted alternative

This paper discusses -admissiblility and d-admissiblity which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for -admissibility is presented. When =1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min (₁, ₁) = 0 versus min (₁, ₁) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and -admissibility are shown. Finally, the case of 1/m is discussed in brief.     

A review on speciation of iodine-129 in the environmental and biological samples

As a long-lived beta-emitting radioisotope of iodine, ¹²⁹I is produced both naturally and as a result of human nuclear activities. At present time, the main part of ¹²⁹I in the environment originates from the human nuclear activity, especially the releases from the spent nuclear fuel reprocessing plants, the ¹²⁹I/¹²⁷I ratios have being reached to values of 10⁻¹⁰ to 10⁻⁴ in the environment from 10⁻¹² in the pre-nuclear era. In this article, we review the occurrence, sources, inventory, and concentration level of ¹²⁹I in environment and the method for speciation analysis of ¹²⁹I in the environment. Measurement techniques for the determination of ¹²⁹I are presented and compared. An overview of applications of ¹²⁹I speciation in various scientific disciplines such as radiation protection, waste depository, and environmental sciences is given. In addition, the bioavailability and radiation toxicity (dose to thyroid) of ¹²⁹I are discussed.     

Statistical Estimation of the Shannon Entropy

The behavior of the Kozachenko–Leonenko estimates for the(differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L~2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.     

Singular Points and an Upper Bound of Medians in Upper Semimodular Lattices

Order - Given a k-tuple P=(x 1,x 2,...,x k ) in a finite lattice X endowed with the lattice metric d, a median of P is an element m of X minimizing the sum ∑ i d(m,x i ). If X is an upper...     

非参数秩检验在宿舍因素对学风影响中的应用

学风建设是大学教育教学管理中的重要环节,对学生的学习成绩、顺利毕业和就业等都有至关重要的影响。宿舍是学生学习和生活的重要场所,本文应用非参数统计秩检验和中位数检验研究了宿舍对学生学业成绩的影响,得到目前大学宿舍因素对学生学业成绩的影响高度显著,进而建议高等学校应加强学生宿舍管理,把宿舍作为学风建设的重要环节。     

基于小波域中值滤波和运动估计的去隔行算法

本文提出了一种新的自适应去隔行算法,该方法首先将小波分解引入到去隔行算法的预处理阶段,然后利用运动估计以及混合中值滤波的特点,充分考虑相邻像素间的方向空间相关性,有效保持图像中的边界部分,并减小了运动补偿插值后的误差,尤其是对纹理信息丰富的地方得到了很好的插值效果.实验结果表明,无论是从客观上的信噪比还是主观测评来分析,图像的效果比传统的算法有了提高,能更好的满足人类对画面质量的要求.     

The Median Stabilization Degree of a Median Algebra

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd 1 in terms of forbidden subspaces.     

Combined and Least Squares Empirical Likelihood

In conventional empirical likelihood, there is exactly one structural constraint for every parameter. In some circumstances, additional constraints are imposed to reflect additional and sought-after features of statistical analysis. Such an augmented scheme uses the implicit power of empirical likelihood to produce very natural adaptive statistical methods, free of arbitrary tuning parameter choices, and does have good asymptotic properties. The price to be paid for such good properties is in extra computational difficulty. To overcome the computational difficulty, we propose a least-squares version of the empirical likelihood. The method is illustrated by application to the case of combined empirical likelihood for the mean and the median in one sample location inference.