SIMPLE CONSTRUCTION OF EMBEDDING FREQUENCIES OF TREES AND ROOTED TREES

Kvasnicka V.; Pospichal J.

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SIMPLE CONSTRUCTION OF EMBEDDING FREQUENCIES OF TREES AND ROOTED TREES

机译：树木和树状树木嵌入频率的简单构建

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A unified approach for the calculation of embedding frequencies of trees as well as rooted trees is suggested. It consists of a simple pruning process when marginal vertices are successively removed. The problem of isomorphism between (rooted) trees is solved by making use of Read's linear canonical code. Simple criteria, based on the concept of valence vectors, for verification whether a (rooted) tree can be a subtree of a (rooted) tree are proved. Tables of embedding frequencies of trees and rooted trees through ten and eight vertices, respectively, are presented. The embedding frequencies of rooted trees are useful for construction of descriptors of molecular graphs when the so-called local properties are studied. [References: 29]

机译：建议采用统一的方法来计算树木和生根树木的嵌入频率。当边缘顶点被连续删除时，它包含一个简单的修剪过程。（根）树之间的同构问题通过使用Read的线性规范代码解决。证明了基于价矢量概念的简单标准，用于验证（有根的）树是否可以是（有根的）树的子树。分别列出了通过十个和八个顶点的树木和有根树木的嵌入频率表。当研究所谓的局部特性时，有根树的嵌入频率对于构造分子图的描述符很有用。 [参考：29]

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《Journal of Chemical Information and Computer Sciences》 |1995年第1期|p. 121-128|共8页
作者
Kvasnicka V.; Pospichal J.;
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作者单位

SLOVAK TECH UNIV DEPT MATH BRATISLAVA 81237 SLOVAKIA;

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原文格式 PDF
正文语种 eng
中图分类化学;
关键词
Topological indexes; Cluster-expansion; Neural networks; Enumeration; Chemistry;

机译：拓扑指数;簇扩展;神经网络;枚举;化学;

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1. Embeddings and Other Mappings of Rooted Trees Into Complete Trees [J] . NICHOLAS GEORGIOU Order . 2005,第3期

机译：根树到完整树的嵌入和其他映射
2. Drawing a rooted tree as a rooted y-monotone minimum spanning tree [J] . Mastakas Konstantinos Information Processing Letters . 2021,第Feba期

机译：将一个扎根的树绘制为rooted y-monotone最小生成树
3. Comparison of growth between own-rooted and grafted 'Aikou' mango trees, and the effects of soil volume on the growth, yield, and fruit quality of potted own-rooted trees [J] . M. Fumuro Acta Horticulturae . 2017,第1174期

机译：自身生根与嫁接“Aikou”芒果树的增长比较，以及土壤体积对盆栽生根树木生长，产量和果实品质的影响
4. Comparison of growth between own-rooted and grafted 'Aikou' mango trees, and the effects of soil volume on the growth, yield, and fruit quality of potted own-rooted trees [C] . Annual Meeting of The International Plant Propagators Society . 2017

机译：自身生根嫁接“Aikou”芒果树的增长比较，以及土壤体积对盆栽生根树木生长，产量和果实品质的影响
5. Tree-like structure in graphs and embedability to trees. [D] . Abu-Ata, Muad Mustafa. 2014

机译：图形中的树状结构和树的可嵌入性。
6. Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation [O] . Ayed R. A. Alanzi, James H. Degnan -1

机译：使用近似贝叶斯计算从无根基因树推断有根树种
7. Figure 6: (A) Tree resulted the standard MP analysis of the 98-loci supermatrix of the Great Apes (Hominidae, Primates, Mammalia) constructed using the modified summary of Lehtonen et al. (2011) (see “Materials and Methods” for the details) and a posteriori rooted relatively Papio (length = 12,092, CI = 0.7877, RI = 0.5597); 34,022 characters are constant, and the number of the parsimony-informative characters is equal to 4,311. MP BS values are provided below branches. The only characters with non-ambiguous value of the outgroup (Papio) have been saved within concatenated alignment; (B) the average consensus tree of the score 0.00084 resulted the analysis of the Hennigian forest of the 5,507 trees derived from the binary representation of the 98-loci supermatrix of the Great Apes (Hominidae, Primates, Mammalia) (see “Materials and Methods” for the details); Papio is assumed to be the best all-plesiomorphic group. “Additional…” FORESTER’s output tree file (see “Materials and Methods” for the details) selected for future analyses; (C) the average consensus tree of the score 0.00090 resulted the analysis of the Hennigian forest of the 5,339 trees derived from the modified binary representation of the 98-loci supermatrix of the Great Apes (Hominidae, Primates, Mammalia) (see 6.I. and “Materials and Methods” for the details), but with all 168 trees, which contain the clade (Homo plus Pan) have been removed from the input forest. “Additional…” FORESTER’s output tree file (see “Materials and Methods”) selected for future analyses. [O] . -1

机译：图6：（A）树导致的标准MP分析的98-基因座的类人猿（人科，灵长类动物，哺乳动物），使用莱赫托宁等人的修改的摘要构成的超级矩阵。（2011）（参见细节“材料和方法”）以及相对植根狒狒后验概率（长度= 12092，CI = 0.7877，RI = 0.5597）; 34022个字符是恒定的，并且简约信息的字符数等于4311。下面提供分支MP BS值。与外类群（狒狒）的非模糊值的唯一的字符已被保存的级联对准内; （B）的得分0.00084的平均一致树导致从巨猿（原始人类，灵长类动物，哺乳动物）的98座超级矩阵的二进制表示获得的5507棵的Hennigian森林的分析（见“材料和方法”为细节）;狒狒被认为是最好的全祖征群。 “其他...” FORESTER的输出树文件（请参阅详细信息“材料和方法”），用于进一步的分析; （C）的分数0.00090的平均一致树导致从98个位点的类人猿（人科，灵长类动物，哺乳动物）的超级矩阵（见6.I的改性二进制表示导出的5339种树木的Hennigian森林的分析以及“材料和方法”的详细说明），但所有168棵，其中包含的分支（智人加PAN）已经从输入林中删除。 “其他...” FORESTER的输出树文件（参见“材料和方法”），用于进一步的分析。
8. Counting Binary, Rooted Trees Arboreal Numbers of the First and Second Kind. Ii. A Recursive Formula for Counting N-Ary Rooted Trees [R] . Weston, P., Ryan, H. F. 1966

机译：计算第一类和第二类树的二元树，根树数。二。计算N元根树的递推公式

SIMPLE CONSTRUCTION OF EMBEDDING FREQUENCIES OF TREES AND ROOTED TREES

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