Probabilistic analysis of a parallel algorithm for finding maximal independent sets

We consider a natural parallel version of the classical greedy algorithm for finding a maximal independent set in a graph. This version was studied in Coppersmith, Raghavan, and Tompa and they conjecture there that its expected running time on random graphs of arbitrary edge density of O (log n). We prove that conjecture.     

Digital stochastic control of distributed-parameter systems

This paper presents a method for discrete-time control and estimation of flexible structures in the presence of actuator and sensor noise. The approach consists of complete decoupling of the modal equations and estimator dynamics based on the independent modal-space control technique and modal spatial filtering of the system output. The solution for the Kalman filter gains reduces to that of independent second-order modal estimators, thus permitting real-time digital control of distributed-parameter systems in a noisy environment. The method can be used to control and estimate any number of modes without computational restraints and is theoretically free of observation spillover. Two examples, the first using nonlinear, quantized control and the second using linear, state feedback control are presented.This work was supported by the National Science Foundation, Grant No. PFR-80-20623.     

A planar metamaterial: Polarization independent fishnet structure

We numerically and experimentally investigate a planar metamaterial that is composed of connected cut-wire pairs and continuous wires operating at 21 GHz. The characterization was performed by using the effective medium theory. The existence of negative refraction is concluded from the transmission data of four structures: cut-wire pairs, shorted cut-wire pairs, composite metamaterial, and shorted composite metamaterial.     

A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables

Let {X _i, 1in} be a negatively associated sequence, and let {X* _i , 1in} be a sequence of independent random variables such that X* _i and X _i have the same distribution for each i=1, 2,..., n. It is shown in this paper that Ef( ⁿ _i=1 X _i)Ef( ⁿ _i=1 X* _i ) for any convex function f on R ¹ and that Ef(max_1kn ⁿ _i=k X _i)Ef(max_1kn ^k _i=1 X* _i ) for any increasing convex function. Hence, most of the well-known inequalities, such as the Rosenthal maximal inequality and the Kolmogorov exponential inequality, remain true for negatively associated random variables. In particular, the comparison theorem on moment inequalities between negatively associated and independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population.     

近独立子系系统的统计规律（一）——二维系统统计规律的计算初席封以

利用刚球模型，根据力学规律，对二维近独立子系系统粒子的运动进行了计算机模拟；模拟中，在不同时刻对系统中各粒子的能量和速率进行多次测量，并对测量结果进行统计平均，得到了粒子数不同的力学系统中粒子按能量和速率的分布图；根据所得的分布图形曲线，给出了任意数目的粒子系统的统一的分布函数．从而完全证明了少量粒子构成的力学系统，其长时间行为也具有确定的统计规律．     

正确选择独立回路的两种方法

分析了两种选择独立回路的错误作法,给出了两种正确选择独立回路的方法,即单链回路法和平面网孔法．     

√S=200GeV质子对撞中横质量谱劈裂效应的PYTHIA模拟研究

在质心系能量为200GeV的质子－质子对撞中, 高横质量区域产生的强子横质量谱分裂成两类——重子和介子. 应用PYTHIA产生器进行Monte Carlo分析其内在的物理机制. 模拟结果表明, 这种劈裂效应不仅在弦碎裂模型中出现, 而且独立碎裂模型中也有, 并且在RHIC能区(200GeV)下主要来源于胶子的贡献. 在PYTHIA6.3版本中引入的新的物理机制表明复杂的弦纠缠(string junction)形式可能是这种重子--介子差异的主要原因.     

有机化学实验教学中学生科学探究能力的培养

The ability of scientific inquiry is one of the important abilities of undergraduate students. We have been thinking and exploring to cultivate students' scientific research ability in the course of laboratory teaching. In recent years, we had carried out persistently reform and practice to the laboratory teaching content and the teaching method in organic chemistry, for example, introduction to the frontier of scientific research, exploring the abnormal phenomena of the experiment, organization of experiment discussion, and carrying out the extracurricular research experiments. The above measures can greatly stimulate the students' interest in learning. Their abilities to think, observe, analyze and solve problems were fully developed. The students' ability of scientific inquiry had been cultivated in multiple aspects. The above measures have effectively promoted the improvement of teaching quality of organic chemistry laboratory course, and also supported the training objectives of high-quality innovative talents in chemistry.     

Simple methods for the optimization of complex‐valued kurtosis as a projection index

With the advancement of modern techniques, complex‐valued data have become more important in chemistry and many other areas. The data collected are often multi‐dimensional. This imposes an increasing demand on the tools used for the analysis of complex‐valued data. In multivariate data analysis, projection pursuit is a useful and important technique that in many cases gives better results than principal component analysis. One important projection pursuit variant uses the real‐valued kurtosis as its projection index and has been shown to be a powerful approach to address different problems. However, using the complex‐valued kurtosis as a projection index to deal with complex‐valued data is rare. This is, to a great extent, due to the lack of simple and fast optimization algorithms. In this work, simple and rapidly executed optimization algorithms for the complex‐valued kurtosis used as a projection index are proposed. The developed algorithms have a variety of advantages: no requirement for sphering or strong‐uncorrelation transformation of the data in advance, no assumption for the latent components (source signals) to be circular or non‐circular, search for maxima or minima on users' requirements, and users having the option to choose uncorrelated scores or orthogonal projection vectors. The mathematical development of the algorithms is described and simulated and real experimental data are employed to demonstrate the utility of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.