Binary Event String Analysis: A Compact Numerical Representation of the Event Tree

While the event tree is a useful diagrammatic aid to an appreciation of various event sequence possibilities, it is of a nature that suggests no obvious manner in which the associated probability data may be compiled as computer input. Here, we propose a complementary numerical representation of scenario possibilities which incorporates probability data in a succinct fashion. While its mnemonic properties facilitate the logical development of a system's characteristics, its compactness and unambiguity permit its utilization directly as computer input.     

ESTIMATING THE COMMON MEAN OF A BIVARIATE NORMAL POPULATION

For estimating the common mean of a bivariate normal distribution, Krishnamoorthy & Rohatgi (1989) proposed some estimators which dominate the maximum likelihood estimator in a large region of the parameter space. We consider some modifications of these estimators and study their risk performance.     

欧几里得空间建立对偶原理的一种方法

本文旨在根据欧几里得空间的特征,探求在欧几里得空间建立对偶原理的一种方法.并利用这种方法说明初等几何中仅与度量性质有关本身并无联系的两种命题可以对偶地联系起来.     

Tree-structured subgroup analysis for censored survival data: Validation of computationally inexpensive model selection criteria

The performance of computationally inexpensive model selection criteria in the context of tree-structured subgroup analysis is investigated. It is shown through simulation that no single model selection criterion exhibits a uniformly superior performance over a wide range of scenarios. Therefore, a two-stage approach for model selection is proposed and shown to perform satisfactorily. Applied example of subgroup analysis is presented. Problems associated with tree-structured subgroup analysis are discussed and practical solutions are suggested.     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

清代树木栽培技术及相关文献探析

中国的树木栽培技术源远流长,曾取得过辉煌的成就。清朝时期在对前人的树木栽培技术进行系统总结和归纳的基础上,结合树木栽培的生产实践,编纂出版了几部学术价值高、影响大、实用性强的文献资料。同时这一时期在植物嫁接成活的生理机制研究、嫁接技术、树木移栽、良种选育与新品种培育、实生苗繁殖技术等方面取得了一定的成就,使清代的树木栽培技术更加完善和成熟。     

Search with small sets in presence of a liar

One unknown element of an n-element set is sought by asking if it is contained in given subsets. It is supposed that the question sets are of size at most k and all the questions are decided in advance, the choice of the next question cannot depend on previous answers. At most l of the answers can be incorrect. The minimum number of such questions is determined when the order of magnitude of k is n with <1. The problem can be formulated as determination of the maximum sized l-error-correcting code (of length n) in which the number of ones in a given position is at most k.     

大学校园中植物多样性调查———以福州地区为例简

当前大学校园环境的塑造广泛引起关注,一个大学校园环境塑造的好坏与其植物配置密切相关。对福州地区十个校园环境的植物进行调查,对其多样性进行总结。为植物配置、植材选择及校园环境塑造给予一定的参考及建议。     

Multi-Step Classification Trees

Many algorithms originated from decision trees have been developed for classification problems. Although they are regarded as good algorithms, most of them suffer from loss of prediction accuracy, namely high misclassification rates when there are many irrelevant variables. We propose multi-step classification trees with adaptive variable selection (the multi-step GUIDE classification tree (MG) and the multi-step CRUISE classification tree (MC) to handle this problem. The variable selection step and the fitting step comprise the multi-step method.

We compare the performance of classification trees in the presence of irrelevant variables. MG and MC perform better than Random Forest and C4.5 with an extremely noisy dataset. Furthermore, the prediction accuracy of our proposed algorithm is relatively stable even when the number of irrelevant variables increases, while that of other algorithms worsens.