Doubling bialgebras of rooted trees

The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by Connes and Kreimer using admissible cuts, and the second is defined by Calaque, Ebrahimi-Fard and the second author using contraction of trees. In this article, we define the doubling of these two spaces. We construct two bialgebra structures on these spaces which are in interaction, as well as two related associative products obtained by dualization. We also show that these two bialgebras verify a commutative diagram similar to the diagram verified Calaque, Ebrahimi-Fard and the second author in the case of rooted trees Hopf algebra, and by the second author in the case of cycle-free oriented graphs.     

The topological structure of 2D disordered cellular systems

We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged concentrically around a germ cell. We single out the most significant parameters that characterize statistically the organization of these patterns. Universality and specificity in disordered cellular structures are discussed. Received: 23 September 1997 / Received in final form: 14 January 1998 / Accepted: 29 January 1998     

Structure characteristics of electrical treeing in XLPE insulation under high frequencies

Electrical tree structure is one of the most important influencing factors for electrical treeing characteristics in polymers. In this paper, we focused on the structure characteristics of electrical treeing in cross-linked polyethylene (XLPE) insulation under high-frequency voltages. The tree structure characteristics include structure distribution characteristics and structure conversion characteristics. The influences of voltage, frequency, and pin-plane spacing on tree structure characteristics were analyzed based on the experimental results. It can be concluded that tree structures regularly change with the local electric field and frequency. The electric field in a very small zone near the needle tip is an important influencing factor for the formation of bush-like trees, and the lowest frequencies for the observed pure-vine-like trees increased with voltage. For double-structure trees, the local electric field at the transition location of the two structures remained almost unchanged with voltage and pin-plane spacing, but obviously increased with frequency. In order to investigate the relations of the growth rate and fractal dimension with tree structure characteristics, a new parameter, the energy threshold W_t, has been introduced and calculated for different tree structures.     

Application of charge simulation method for investigation of effects of the trees on lightning protection of structures

The paper deals with the principles of lightning protection of structures. The principles have been formulated on the base of application of charge simulation method (CSM) in order to investigate the effects of trees on lightning protection of buildings. The simulation results and laboratory test on scale model demonstrate the benefit of this method of computation lightning protection for structures.     

发展在XLPE电缆绝缘内外侧的电树枝

以XLPE高压电力电缆内外侧绝缘中的电树枝特性为研究对象，通过分析电树枝引发与生长的统计实验规律和采用扫描电子显微镜分析发现，由于不同结晶状态的影响，电缆绝缘内外侧的电树枝特性存在很大的差异.引发于绝缘内侧电树枝引发时间短、生长速度快、电树枝形状具有多样性；起始于绝缘外侧的电树枝不仅引发时间长、生长速度极慢，而且电树枝形状(结构)比较单一.并对这两个位置电树枝的引发和生长机理进行了探讨. 关键词： 电树枝 结晶状态 统计规律 内侧和外侧绝缘层     

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。     

Construction and studies of a new class of reciprocal trees: interknitting of the Pascal's triangle

A method of construction of a new class of trees with reciprocal pairs of eigenvalues (λ, 1/λ) has been developed. They are derived from star graphs and can be symbolized as K _{1, n ?1} + n(p) + mK ₂ (1 ≤ m ≤ n ? 1 except for n = 1). The trees are minimally Kekulenoid and hence contain reciprocal pairs of eigenvalues in their eigenspectra. The characteristic polynomial coefficients of these trees with given values of n and m are shown to be obtainable by appropriate use of the Pascal's triangle. A general formula for this purpose has been developed. An analytical formula for the Wiener indices of such trees in terms of m and n has been derived and some consequences of this formula are presented. The relevance of these trees to real molecular structures is discussed. The trees have been shown to be useful in observing the subspectrallity of two series of IPR fullerenes of formulae C_{50+10 n} and C_{60+12 n} (n is a positive integer).     

像元尺度林地冠层二向反射特性的模拟研究

计算机模拟模型是以计算机图形学方法生成的植被真实结构场景为基础,利用辐射度方法模拟植被冠层的辐射特性。文章将这种方法拓展到遥感像元尺度林冠二向反射光谱特性的模拟。由于模拟像元尺度的林地真实场景需要大量面元组成,而辐射度方法无法承受如此多的面元计算。为了解决这一问题,文章提出了简化树冠结构的思想,将树冠抽象为椭球体,根据光在真实树冠内部能量传输的特点为简化的椭球体面元赋值,并将真实树冠间的间隙率考虑其中,结合几何光学模型的思想完成了像元尺度林地场景冠层二向反射光谱特性的模拟。并将模拟结果与GOMS模型、MISR多角度遥感数据进行了比较,取得了比较好的结果。研究结果对多角度遥感数据应用和植被冠层结构参数反演具有重要价值。     

Fabrication of self-standing nanowires, nanodendrites, and nanofractal-like trees on insulator substrates with an electron-beam-induced deposition

Self-standing tungsten nanowires, nanodendrites, and nanofractal-like trees were fabricated on insulator (Al₂O₃) substrates with a process of electron-beam-induced decomposition in a transmission electron microscope. The conditions for fabricating different morphologies are described. The fabricated structures are characterized with high-resolution transmission electron microscopy and X-ray energy-dispersive spectroscopy. A high concentration of tungsten and a high crystallinity of the structure are confirmed. The growth process is discussed, involving charges produced on the surface of the substrate and the behavior of precursor molecules under electron-beam irradiation. The formation of these structures is considered to relate to nanoscaled unevenness of the charge distribution on the surface of the substrate, movement of charges to the convex surface of the substrate, and accumulation of charges at the tips of the grown structures. PACS 81.07.-b; 07.78.+s; 81.15.Gh; 81.16.-c     

Random Sequential Adsorption on Random Trees

When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. Two models which have frequently been studied are the “dimer model” and the “blocking model”, and rather complete solutions for these are known on fixed tree structures or Bethe lattices. In this paper comparisons are made between the occupation probabilities for vertices between fixed and random trees.     

Topological properties of phylogenetic trees in evolutionary models

The extent to which evolutionary processes affect the shape of phylogenetic trees is an important open question. Analyses of small trees seem to detect non-trivial asymmetries which are usually ascribed to the presence of correlations in speciation rates. Many models used to construct phylogenetic trees have an algorithmic nature and are rarely biologically grounded. In this article, we analyze the topological properties of phylogenetic trees generated by different evolutionary models (populations of RNA sequences and a simple model with inheritance and mutation) and compare them with the trees produced by known uncorrelated models as the backward coalescent, paying special attention to large trees. Our results demonstrate that evolutionary parameters as mutation rate or selection pressure have a weak influence on the scaling behavior of the trees, while the size of phylogenies strongly affects measured scaling exponents. Within statistical errors, the topological properties of phylogenies generated by evolutionary models are compatible with those measured in balanced, uncorrelated trees.     

The application of computational fluid dynamics to pedestrian level wind safety problem induced by high-rise buildings

In this paper, the pedestrian level wind safety problem induced by high-rise buildings has been studied using the computational fluid dynamics (CFD) codes Fluent. The verification by use of wind tunnel data shows that Fluent can fairly reproduce the flow field in the areas adjacent to the structure when a realizable k-ε turbulence model is adopted in calculations. The results of the numerical simulations including seven cases show that the existence of high-rise buildings does increase the wind hazard probability at the pedestrian level; furthermore, the wind direction, the geometric size of structures and the layout of structures can obviously affect the pedestrian level wind environment. However, trees on the pavement do not contribute much in reducing the wind hazard probability.     

高频电压下交联聚乙烯电缆绝缘中电树枝生长的动力学模型

针对高压交联聚乙烯电缆绝缘试样,在1000—2000Hz 10kV峰值正弦电压下,采用计算机实时显微数字摄像技术进行了电树枝培养实验.基于半结晶绝缘材料中电树枝生长机理和电树枝结构的分形特征,提出了一个在高频范围定量预测电应力驱动下交联聚乙烯电缆绝缘中电树枝生长特性的动力学模型,获得了电树枝生长率方程和从电树枝生长到击穿过程的寿命公式.将该模型预测值与实验中获得的电树枝生长规律实验数据进行比较,其结果有较好的一致性,表明提出的模型化方法可以应用到交联聚乙烯电缆绝缘中电树枝老化规律的定量分析研究中. 关键词： 交联聚乙烯电缆绝缘 电树枝 施压频率 动力学模型     

Verification of Annual Growth Rings in Egyptian Trees by C-14 Method

Annual growth rings in trees were thought to be due to sharp seasonal variations in the precipitation rates during the year. Accordingly temperate zone trees such as Egyptian trees were supposed to be away from this phenomenon. The temperate zones which are ment here are those of no sharp seasonal variations in the precipitation rates. The present study applied carbon-14 dating to prove that the growth rings in some Egyptian trees are annual. The method was based on the tropospheric measurements of C-14 during the period 1954–1981. C-14 exhibited a sharp peak resulting from the ever greater series of nuclear tests during 1963–1965. The presence of this peak for Egyptian trees proved that they form annual growth rings.     

Large Deviations for Random Trees

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.     

Self-contained algorithms to detect communities in networks

The investigation of community structures in networks is an important issue in many domains and disciplines. In this paper we present a new class of local and fast algorithms which incorporate a quantitative definition of community. In this way the algorithms for the identification of the community structure become fully self-contained and one does not need additional non-topological information in order to evaluate the accuracy of the results. The new algorithms are tested on artificial and real-world graphs. In particular we show how the new algorithms apply to a network of scientific collaborations both in the unweighted and in the weighted version. Moreover we discuss the applicability of these algorithms to other non-social networks and we present preliminary results about the detection of community structures in networks of interacting proteins.Received: 7 November 2003, Published online: 14 May 2004PACS: 89.75.Hc Networks and genealogical trees - 87.23.Ge Dynamics of social systems - 87.90. + y Other topics in biological and medical physics     

Decision Rules Derived from Optimal Decision Trees with Hypotheses

Conventional decision trees use queries each of which is based on one attribute. In this study, we also examine decision trees that handle additional queries based on hypotheses. This kind of query is similar to the equivalence queries considered in exact learning. Earlier, we designed dynamic programming algorithms for the computation of the minimum depth and the minimum number of internal nodes in decision trees that have hypotheses. Modification of these algorithms considered in the present paper permits us to build decision trees with hypotheses that are optimal relative to the depth or relative to the number of the internal nodes. We compare the length and coverage of decision rules extracted from optimal decision trees with hypotheses and decision rules extracted from optimal conventional decision trees to choose the ones that are preferable as a tool for the representation of information. To this end, we conduct computer experiments on various decision tables from the UCI Machine Learning Repository. In addition, we also consider decision tables for randomly generated Boolean functions. The collected results show that the decision rules derived from decision trees with hypotheses in many cases are better than the rules extracted from conventional decision trees.     

Morphology of electrical trees in silicon rubber

The main cause of degradation and breakdown in silicon rubber (SIR) is electrical treeing. Based on a series of experiments, this paper discusses the morphology of the electrical trees. The types of morphology of electrical trees in SIR are concluded. The effective factors of the tree initial type are explored. And the propagation characteristics are also studied through long-term electrical tree ageing experiments. These results are also compared with the electrical trees occurred in on-site cable accessories and those in PE which are more familiar to researchers. Based on those experiment results, an explanatory mechanism is proposed.