关于乘积Sombor指数的极值(分子)树

拓扑指数是一类可以用来预测化合物的物理化学性质的数值不变量, 其并被广泛用于量子化学、分子生物学和其他研究领域. 对于一个顶点集为$V(G)$、边集为$E(G)$的(分子)图$G$, 其Sombor指数定义为$SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{G}^{2}(u)+d_{G}^{2}(v)}$, 其中$d_{G}(u)$表示顶点$u$在$G$中的度. 相应地, 乘积Sombor指数定义为$\prod\nolimits_{SO}(G)= \prod\limits_{uv\in E(G)}\sqrt{d_{G}^{2}(u)+d_{G}^{2}(v)}$. 分子树是最大度$\Delta\leq 4$的树. 在本文中, 我们首先确定了乘积Sombor指数最大的分子树, 然后我们确定了乘积Sombor指数的前十三小的(分子)树.     

取代羧酸pKa的分子树拓扑研究

基于非氢原子i的酸性点价(δai)建构分子树拓扑指数(mT)及其分支指数(mTC)和叶指数(mTx),并提出表征诱导效应的叶指数(mT′x).通过最佳变量子集算法获得38种羧酸的pKa与0TC、1TC、0T′x的回归方程:pKa=3.0352-1.25700T′x-0.15540TC+0.07811TC,R=0.9766.通过Jackknife法检验,该模型具有总体稳健性.优于文献的七元最佳回归模型(R=0.957),与其分子力学方法(CoMFA)结果(R=0.988)较为接近.结果表明,所建拓扑指数是合理的,具有科学性基础.     

Vertices contained in every minimum dominating set of a tree

In this article we begin the study of the vertex subsets of a graph G which consist of the vertices contained in all, or in no, respectively, minimum dominating sets of G. We characterize these sets for trees, and also obtain results on the vertices contained in all minimum independent dominating sets of trees. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 163‐177, 1999     

Cryptocurrency Market Consolidation in 2020–2021

Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself.     

不交树:对网络系统和故障树进行定量分析的新方法

本文提出了一个对事件集建造不交树的方法。这个方法中通过分离独立项和提取公因子使割集(路集)的项数和阶次迅速下降。所建成的不交树中所有分支互不相交,因此可由直接计算求得顶事件的发生概率。给出了应用例子。讨论了向多态系统的推广以及近似计算方法。     

Criterion for a chain of σ-processes to be the composition of triangular chains

The purpose of this paper is to establish a topological criterion for a chain of spheres in a two-dimensional complex manifold to be a composition of so-called triangular chains. Explicit formulas are given for the relevant topological characteristics of chains. Certain corollaries of this criterion related to the Jacobian conjecture are discussed. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 643–653, May, 1999.     

约束最小生成树问题研究

本文对约束最小生成树问题提出一个算法,它的计算复杂性是O(n3)．然后把约束最小生成树作为约束Steiner最小树的一个近似解,则近似解的性能比为3?/2．     

树上马氏链场的若干极限性质

该文引进广义Ｂｅｔｈｅ树和广义Ｃａｙｌｅｙ树的概念,并研究其上马氏链场关于状态和状态序偶出现频率的强极限定理,作为主要结果的推论,得到Ｂｅｔｈｅ树和Ｃａｙｌｅｙ树上马氏链场的ＳｈａｎｎｏｎＭｃＭｉｌｌａｎ定理．证明中采用了研究概率论强极限定理的一种新的方法．     

住院患者病情危重度的分类决策树研究

目的　应用分类决策树对各类疾病住院患者的病情进行分类和评价。方法　采用SPSSAnswerTree分类软件和CHAID算法,用1244887例住院患者的病案首页数据,通过确定分类目标变量、预测变量、决策树的生长和修剪规则,建立覆盖所有病种的危重度分类模型。结果　建立了163个基于病种的分类模型,每个病种都形成了若干个危重度等级,共产生了636个危重度类别,每个类别对应一个危重度分值。经新样本考核,该病情指标对治疗结果、医院规模有一定预测能力,且与住院费用相关。结论　病情分类结果能够反映住院患者的相对病情,可作为病情标准化的依据,用于医疗服务质量效率评价。