Non binary partially neighbor balanced designs for circular blocks

ABSTRACT

Neighbor designs are recommended for the cases where the performance of treatment is affected by the neighboring treatments as in biometrics and agriculture. In this paper we have constructed two new series of non binary partially neighbor balanced designs for v = 2n and v = 2n+1 number of treatments, respectively. The blocks in the design are non binary and circular but no treatment is ever a neighbor to itself. The designs proposed here are partially balanced in terms of nearest neighbors. No such series are known in the literature.     

Some Methods of Replacing the Nearest Neighbor Method

In this article, two classifiers, which generalize the nearest neighbor method, are introduced and studied. The first of them is based on calculating the distances to all objects from a learning sample. The second one additionally considers directions of the objects. Both of them have locally nonlinear classification borders. A number of real and artificial datasets and methods of error estimation are used.     

Minimal Neighbor Designs in Linear Blocks

Neighbor designs are useful to neutralize the neighbor effects. In literature, most of the constructed neighbor designs are in circular blocks but linear blocks have more practical application in field experiments. In this article, some infinite series of minimal neighbor designs are constructed in proper linear blocks. There are many situations where minimal neighbor designs cannot be constructed in proper linear blocks. To overcome this problem neighbor designs in improper linear blocks and GN₂-designs in proper linear blocks are constructed.     

节点集重要性测度——综合法及其在知识共享网络中的应用

在具有社会关系结构的经济系统及通讯网络系统等许多现实的系统中,人们经常关注节点集在系统中的重要性问题.在分析如何有效反映网络中节点集重要性的基础上,针对节点赋权网络,利用节点集删除的研究方法,建立节点集重要性的综合测度数学模型;然后,借助于图的距离矩阵的计算方法设计该模型的算法;最后,给出该方法在知识共享网中的应用.     

Distributed inference for two-sample U-statistics in massive data analysis

This paper considers distributed inference for two-sample U-statistics under the massive data setting. In order to reduce the computational complexity, this paper proposes distributed two-sample U-statistics and blockwise linear two-sample U-statistics. The blockwise linear two-sample U-statistic, which requires less communication cost, is more computationally efficient especially when the data are stored in different locations. The asymptotic properties of both types of distributed two-sample U-statistics are established. In addition, this paper proposes bootstrap algorithms to approximate the distributions of distributed two-sample U-statistics and blockwise linear two-sample U-statistics for both nondegenerate and degenerate cases. The distributed weighted bootstrap for the distributed two-sample U-statistic is new in the literature. The proposed bootstrap procedures are computationally efficient and are suitable for distributed computing platforms with theoretical guarantees. Extensive numerical studies illustrate that the proposed distributed approaches are feasible and effective.