脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

无标度网络上队列资源分配研究

研究了节点队列资源有限的条件下,无标度网络上的信息流动力学过程,发现了网络由自由流通到拥塞的相变现象,提出了一种基于节点度的队列资源分配模型.模型的核心是使节点i的队列长度与kβi成正比(ki为节点i的度,β为分配参数).仿真结果表明,在网络使用最短路径算法进行信息包传送的条件下,β近似等于1.25时队列资源分配最合理,网络容量最大,且该最佳值与队列总资源多少以及网络的规模无关.     

一种基于重标极差方法的动力学结构突变检测新方法

提出了一种针对相关性时间序列动力学结构突变检测的新方法——滑动移除重标极差分析.数值试验表明,新方法能够准确的检测出理想序列中的动力学结构突变,其检测结果对于子序列的长度依赖性较小,而且具有很强的抗噪能力,弥补了滑动去趋势波动分析的不足. 关键词： 标度指数 滑动移除重标极差分析 滑动去趋势波动分析 动力学结构突变     

Optimal Capacity Allocation on Heterogeneous Complex Transport Networks

We study how the node delivering capacity is allocated so that the traffic transport efficiency can be enhanced maximally. Network heterogeneity of degree distribution and processing delay of the traffic are considered. An explicit analytical solution is provided, which is based on the M/M/1 queueing theory and optimization principle, provided that the network structure and routing strategy are given. In particular, we extend the relevant conclusions in the literature [Europhys. Lett. 83 （2008） 28001]. Finally, an order parameter simulation example by comparing results with those obtained via simple capacity allocation in large Barabasi—Albert （BA） scale-free network is provided to illustrate the effectiveness of the theoretical results.     

Condensation of Self-Driven Particles in Scale-Free Networks

A new simple model of self-driven particles in scale-free networks is introduced to understand the emergence of condensation in the natural world. In the model, at each time step, particles are driven to choose their next habitats according to the particle numbers at both the present habitats and neighbors. It is found that the hub effect results in the condensation. The present numerical results as well as the theoretical analysis of condensation transition show the criterion of condensation. Both simulations and theoretical analysis display that there are three phases for different hopping probabilities δ： non-condensation （δ〈δc）, partial condensation （δc≤ δ〈1）, and complete condensation （δ≥δc＇= 1）, and the mean occupation particle number at the stationary state is also obtained. Moreover, the noise effect on self-driven particles is studied, and it makes particle numbers at nodes tend towards being identical.     

基于二项分布随机增长的无标度网络

提出—个具有随机增长的无标度网络模型．该模型的演化规则仍然是BA模型的增长和择优连接,但是每一时间间隔添加到网络中的边数是—个具有二项分布的随机变量．通过率方程方法,本文证明了该网络的度分布具有幂律尾部,该模型生成了—个无标度网络．     

相对论重离子碰撞中分形特性的研究

用AMPT模型产生5000个质心能量为(1/2)S=200GeV的Au-Au碰撞事件,计算了其多粒子末态系统三个不同方向的一维阶乘矩,发现三个不同平面的Hurst指数在误差范围内相等。对三维相空间进行各向同性分割,得到的阶乘矩显示出了良好的标度特性,这表明相对论重离子碰撞的末态粒子相空间是自相似的分形结构。     

三标度AHP法在核应急决策中的应用

核事故发生时,采取正确的应急决策可以减轻事故的后果和危害.考虑到核应急决策的多目标性和模糊性,并针对传统AHP法的不足,利用三标度AHP法建立了多层次应急决策评估模型.模型较大程度的减小了评价的主观性,具有操作性强、稳定性好的特点.将模型与模糊层次模型计算结果进行比较,二者对方案的优劣排序是一致的.但模型在对最优方案的取舍上分辨率较高,对核应急决策具有实际的指导意义.     

Calculation of the photoelectron spectra under a scaling transform

By solving the time-dependent Schro¨dinger equation, the dependence of photoelectron energy spectra on the binding energy of targets, wavelength and the intensity of laser pulse is exhibited and a scaling law of kinetic energy spectra of both the direct and the rescattered photoelectrons is concluded. The scaling law provides a convenient tool to determine the equivalent photoionization process of various atoms or molecules in various laser fields. The verification of the scaling law by independent methods provides incontestable support to the validity of the scaling law.     

Opinion Spreading with Mobility on Scale-Free Networks

A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.