关于Steiner树的一个不等式

本文部分地改进了堵丁柱、黄光明所证明的Gilbert-Pollak关于Steiner树的一个猜想,提出一个新的不等式。     

Limsup deviations on trees

The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Sσ = ∑θ＜r≤σXr. We introduce and study the oscillations of the walk:Exact Hausdorff dimension of the set of such ξ 's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.     

Dirac's Condition for Completely Independent Spanning Trees

Two spanning trees T₁ and T₂ of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T₁ and T₂ are internally disjoint. In this article, we show two sufficient conditions for the existence of completely independent spanning trees. First, we show that a graph of n vertices has two completely independent spanning trees if the minimum degree of the graph is at least . Then, we prove that the square of a 2‐connected graph has two completely independent spanning trees. These conditions are known to be sufficient conditions for Hamiltonian graphs.     

Moments of first hitting times for birth-death processes on trees

An explicit and recursive representation is presented for moments of the first hitting times of birth-death processes on trees. Based on that, the criteria on ergodicity, strong ergodicity, and l-ergodicity of the processes as well as a necessary condition for exponential ergodicity are obtained.     

当匹配数很小时具有最小拉普拉斯谱半径的树

考虑了具有最小拉普拉斯谱半径的树的问题. 并确定了当匹配数很小时具有最小拉普拉斯谱半径的树.     

基于光谱分析的果树树种辨识研究

利用冠层光谱反射率数据(R_λ),对处于果实成熟期的七种挂果果树的树种进行了辨识研究。通过光谱数据重采样、植被指数求算等相关数据处理,比较了六种卫星传感器与四种植被指数对果树树种的辨识效能,并在优选数据形式、优化模型参数的基础上,建立了辨识果树树种的BP神经网络模型。主要结论为：(1)六种卫星传感器辨识果树树种的效能由强到弱的排列顺序为：MODIS,ASTER,ETM+,HRG,QUICKBIRD,IKONOS;(2)在四种植被指数中,RVI对果树树种的辨识效能最强,其次是NDVI,SAVI与DVI的辨识效能相对较弱;(3)用MODIS或ETM+传感器的近红外通道与红光通道上的反射率数据,求算的RVI与NDVI对果树树种的辨识效能相对较强;(4)在R_λ及其22种变换数据中,波长间隔设为9 nm的d1[log(1/R_λ)] ,是建立BP神经网络模型的首选数据形式;(5)利用波长间隔设为9 nm的d1[log(1/R_λ)] 这一数据形式,建立了辨识果树树种的3层BP神经网络模型。     

近红外光谱技术快速预测泡桐活立木年轮密度

应用近红外光谱分析技术主要对兰考泡桐活立木年轮密度进行了研究。取样时采用无损的方式,即不伐木,只从样木胸径处钻取直径为5 mm的木芯;用近红外光谱仪采用自动进级式采集样品光谱,波谱范围为350～2 500 nm;密度值采用水银体积仪测量;校正模型和预测模型建立与分析采用偏最小二乘和完全交互验证法。研究结果表明,中径级和大径级泡桐所选年轮数与近红外光谱值之间均存在很好的相关关系,预测模型相关系数分别达0.88和0.91;中径极的泡桐年轮密度与近红外光谱的校正模型和预测模型相关系数分别达到0.90和0.83,校正标准误差(SEC)和预测标准误差(SEP)分别为0.012和0.016。由此可见,该法可简单、快速、无损的预测中径级即接近采伐龄泡桐活立木的年轮密度。     

Mood Disorder Detection in Adolescents by Classification Trees,Random Forests and XGBoost in Presence of Missing Data

We apply tree-based classification algorithms, namely the classification trees, with the use of the rpart algorithm, random forests and XGBoost methods to detect mood disorder in a group of 2508 lower secondary school students. The dataset presents many challenges, the most important of which is many missing data as well as the being heavily unbalanced (there are few severe mood disorder cases). We find that all algorithms are specific, but only the rpart algorithm is sensitive; i.e., it is able to detect cases of real cases mood disorder. The conclusion of this paper is that this is caused by the fact that the rpart algorithm uses the surrogate variables to handle missing data. The most important social-studies-related result is that the adolescents’ relationships with their parents are the single most important factor in developing mood disorders—far more important than other factors, such as the socio-economic status or school success.