On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n²). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n).     

DIMENSIONS FORRANDOM SELF——CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets.     

Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ^d (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d2.     

A mean-field,effective medium theory of random binary alloys III. The ising model with competing interactions

The Ising model with competing interactions is studied in a mean field effective medium approach. The phase diagram of such model alloys is studied. We conclude that for all ratios of the competing interaction moments, a spin glass phase always exists at low temperatures for certain concentration regimes.     

Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

LIBS中药材石斛等级识别研究

石斛是一种常用的中药材,经常使用新鲜的或干燥的茎条入药,有益胃生津、滋阴清热的效果。近年来,药理学研究探索出石斛具有抗白内障、抗氧化、抗肿瘤、提高免疫力的作用,其在许多病例中疗效显著,引起了国内外学者的关注,然而不同时间采集的石斛中氨基酸、微量元素等含量各不同,其对应药用价值,价格也不同,因此石斛价格等级分辨的研究具有重要意义。为快速鉴别不同价格、不同药效的石斛,研究了随机森林分类模型结合激光诱导击穿光谱技术(LIBS)对石斛价格等级进行分析建模。选取5个等级的石斛样品进行建模,为了对样品进行精确稳定分析,所有石斛样品均通过粉碎压片减小实验误差。采用1 064 nm波长的Nd∶YAG脉冲激光器作为激发光源,设置激光脉冲能量50 mJ,探测延时1μs,采集五个等级石斛样本的光谱数据,每个等级的样本采集40组光谱,共200组数据,并采用归一化处理,使所有的光谱数据转换到-1~1之间。采用归一化处理后的光谱数据进行主成分分析,通过主成分分析获得前7个主成分的得分矩阵,其累计解释95.24%的光谱信息。将选取的7个主成分作为输入,建立波段为220~880 nm的随机森林鉴别模型。并将石斛样本编号打乱,任意选取50%的光谱数据作为训练集,剩下50%的光谱数据作为测试集,默认决策树个数ntree为500,分裂属性集中属性个数mtry为5,建立模型对不同等级的石斛进行分类。等级一、二、三、四、五的识别率分别为95.45%, 100%, 78.26%, 94.12%和85%,平均识别率为90.57%。为提高识别率,研究了不同的ntree和mtry对分类模型的影响,利用袋外数据误差率估计对随机森林的两个参数进行了优化。选择ntree为300,mtry为1,等级一、二、三、四、五的识别率分别为100%, 100%, 92.31%, 100%和90%,平均识别率为96.46%,识别率提高了5.89%。综上所述,采用LIBS技术结合优化后的随机森林模型鉴别石斛等级具有一定的可行性,为未来快速鉴定不同价格的石斛等级分类提供了可行性的判别系统。     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Emergence of complex networks from diffusion on fractal lattices. A special case of the Sierpinski gasket and tetrahedron

A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks.     

Randomly chosen chaotic maps can give rise to nearly ordered behavior

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable.     

Quasiclassical trajectory theoretical study on the chemical stereodynamics of the O(~1D)+H_2→OH+H reaction and its isotopic variants (HD,D_2)

The quasiclassical trajectory (QCT) method is used to study stereodynamic information about the reaction O ( 1 D) + H 2 →OH + H on the DK (Dobbyn and Knowles) (1 1 A' ) ab initio potential energy surface (PES). A wide scale of collision energy (E c ) from 0.05 eV to 0.5 eV is considered in the dynamic calculations. To reveal the rovibrational excitation effect, calculations at a collision energy of 0.52 eV are carried out for the v = 0 ～ 5, j = 0 and v = 0, j = 0 ～ 15 initial states. The two popularly used polarization-dependent differential cross sections (PDDCSs), dσ 00 /dω t (0, 0) and dσ 20 /dω t (2, 0), and two angular distributions, P(θ r ) and P( r ) are calculated to obtain an insight into the alignment and the orientation of the product molecules. From the calculations, we can obtain that the alignment of the OH product is weaker at high collision energy and becomes stronger with the increase of initial vibrational level, and it is almost insensitive to the initially rotational excitation. Influences of the mass values of isotopes (HD, D 2 ) on the stereodynamics are also shown and discussed. Comparisons between available theoretical results and experimental results are made and discussed.