The runt test for multimodality

Single linkage clusters on a set of points are the maximal connected sets in a graph constructed by connecting all points closer than a given threshold distance. The complete set of single linkage clusters is obtained from all the graphs constructed using different threshold distances. The set of clusters forms a hierarchical tree, in which each non-singleton cluster divides into two or more subclusters; the runt size for each single linkage cluster is the number of points in its smallest subcluster. The maximum runt size over all single linkage clusters is our proposed test statistic for assessing multimodality. We give significance levels of the test for two null hypotheses, and consider its power against some bimodal alternatives. Research partially supported by NSF Grant No. DMS-8617919.     

The complexity of reconstructing trees from qualitative characters and subtrees

In taxonomy and other branches of classification it is useful to know when tree-like classifications on overlapping sets of labels can be consistently combined into a parent tree. This paper considers the computation complexity of this problem. Recognizing when a consistent parent tree exists is shown to be intractable (NP-complete) for sets of unrooted trees, even when each tree in the set classifies just four labels. Consequently determining the compatibility of qualitative characters and partial binary characters is, in general, also NP-complete. However for sets of rooted trees an algorithm is described which constructs the “strict consensus tree” of all consistent parent trees (when they exist) in polynomial time. The related question of recognizing when a set of subtrees uniquely defines a parent tree is also considered, and a simple necessary and sufficient condition is described for rooted trees. This work was supproted by the Alexander von Humoldt-Stiftung. I wish to thank Andreas Dress, Hans-Jürgen Bandelt and the referees for their helpful comments.     

宝华山栎林生态系统乔木层的营养元素循环

本文主要讨论宝华山栎林群落乔木层营养元素的含量和循环。文中详细给出了乔木层现存量、年吸收及年存留中N、P、K、Ca、Mg五种元素的量和分配。     

广西海岸白骨壤红树植物地上部生物量的相关分析

1992年3月在广西北海半岛大冠沙白骨壤群落研究了白骨壤植株的测树因子跟地上部生物量间的相关性。结果显示,由于白骨壤植株形态多变,树高通常小于2.0m,树高在估算地上部生物量时并不重要。植株的生物量可较好地用下述方程估算:茎:W=0.8496-0.4429D+0.0748D~2枝:W=-2.2744+1.5595e~(-H)+1.0590C+0.0606D~2叶:W=0.0180D~(2.1294)地上部分生物量:W=-2.4386+0.0081H/LnH+1.4796C+0.0991D~2式中 H 为树高(m),D 为基茎(cm),C 为冠幅(m~2),W 为干重(kg)。文中还给出了利用这些方程估算群落生物量的范例。     

M-回路网络的中心选址

研究含边不交回路网络的中心选址问题,给出了一个求其最小直径支撑树的破圈算法,由此得到求其中心的O(mn)阶算法,这里m是网络中含回路的个数。     

树、森林的顺序存储及转化为二叉树的一个算法

本文提出树,森林的顺序存储的一种方法,同时提出这种顺序存储转化为一棵二叉树的算法。由于树、森林等价于一棵二叉树,从而达到对树、森林的周游。     

二元树结构的容错分析

分析几种二元树结构的容错方法,给出了容错的重构规则。     

组织协作网与决策树

基于组织基本组成元素(决策者、平台和任务)的定义描述了组织协作网与决策树。通过对组织协作网与决策树的描述分析提出了组织结构设计的新思路:基于决策个体在任务上的协作关系设计最佳的决策树(组织决策的层次结构)。并描述了从组织协作网到决策树的生成过程,对生成过程的求解采用了优化协作树算法。针对案例对决策树的产生进行了求解和分析。     

Model Checking Workflow Net Based on Petri Net

The soundness is a very important criterion for the correctness of the workflow. Specifying the soundness with Computation Tree Logic （CTL） allows us to verify the soundness with symbolic model checkers. Therefore the state explosion problem in verifying soundness can be overcome efficiently. When the property is not satisfied by the system, model checking can give a counter-example, which can guide us to correct the workflow. In addition, relaxed soundness is another important criterion for the workflow. We also prove that Computation Tree Logic ＊ （CTL ＊ ） can be used to character the relaxed soundness of the workflow.     

A Shortest Path Problem

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