Analysis of precipitation characteristics of South and North China based on the power-law tail exponents

Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.     

应力导致的薄栅氧化层漏电流瞬态特性研究

分别研究了FN隧穿应力和热空穴(HH)应力导致的薄栅氧化层漏电流瞬态特性.在这两种应力条件下,应力导致的漏电流(SILC)与时间的关系均服从幂函数关系,但是二者的幂指数不同.热空穴应力导致的漏电流中,幂指数明显偏离-1,热空穴应力导致的漏电流具有更加显著的瞬态特性.研究结果表明:热空穴SILC机制是由于氧化层空穴的退陷阱效应和正电荷辅助遂穿中心的湮没.利用热电子注入技术,正电荷辅助隧穿电流可被大大地减弱.     

Predicting the long tail of book sales: Unearthing the power-law exponent

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.     

Human dynamics scaling characteristics for aerial inbound logistics operation

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions — that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.     

Power-law regularities in human language

Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf’s law and Heaps’ law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.     

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.     

基于复杂网络理论的微博用户关系网络演化模型研究

微博给人们提供便利的同时也产生了较大的负面影响.为获取微博谣言的传播规律,进而采取有效措施防控其传播,本文基于复杂网络理论研究微博用户关系网络的内部特征,提出一种微博用户关系网络演化模型,借助于平均场理论,分析该演化模型的拓扑统计特性,以及谣言在该演化模型上的传播动力学行为.理论分析和仿真实验表明,由该模型演化生成的微博用户关系网络具有无标度特性.度分布指数不仅与反向连接概率有关,而且还取决于节点的吸引度分布.研究还发现,与指数分布和均匀分布相比,当节点吸引度满足幂律分布时,稳态时的谣言传播程度较大.此外,随着反向连接概率或节点初始连边数量的增加,谣言爆发的概率以及网络中最终接受谣言的节点数量都会明显增大.     

Effects of saving and spending patterns on holding time distribution

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed.Received: 4 September 2003, Published online: 19 November 2003PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 87.23.Ge Dynamics of social systems - 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 02.50.-r Probability theory, stochastic processes, and statistics     

Production, depreciation and the size distribution of firms

Many empirical researches indicate that firm size distributions in different industries or countries exhibit some similar characters. Among them the fact that many firm size distributions obey power-law especially for the upper end has been mostly discussed. Here we present an agent-based model to describe the evolution of manufacturing firms. Some basic economic behaviors are taken into account, which are production with decreasing marginal returns, preferential allocation of investments, and stochastic depreciation. The model gives a steady size distribution of firms which obey power-law. The effect of parameters on the power exponent is analyzed. The theoretical results are given based on both the Fokker-Planck equation and the Kesten process. They are well consistent with the numerical results.     

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Long-term correlations in hourly wind speed records in Pernambuco, Brazil

We study the statistical properties of hourly wind speed time series detected at four weather stations in the state of Pernambuco, Brazil, in the period 2008-2009. We find that the average and maximum hourly wind speeds deviate from a mutual linear relationship, and that they may be well explained individually by a Weibull distribution, however, with different shape parameter values. On the other hand, the long-term correlations of both of these observables obey the same power-law behavior, with two distinct scaling regimes. Our results agree with previous studies on wind speed series correlations in other regions of the world, which is suggestive of universal behavior.     

An evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike  , show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p$p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p$p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.     

结合可视图的多状态交通流时间序列特性分析

交通流时间序列的研究主要采用数据挖掘和机器学习的方法,这些"黑箱"挖掘方法很难直观反映序列特性.为增强交通流时间序列及其特征分析的可视化性,结合可视图理论来构建交通流时间序列的关联网络,从复杂网络角度实现交通流时间序列的特性分析.在网络构建的过程中,考虑到不同交通状态下交通流表征具有的差异性,首先利用交通流参量的相关性对交通流状态进行分类,然后构建不同交通状态下的时间序列复杂网络,并对这些网络的特征属性给出统计分析,如度分布、聚类系数、网络直径、模块化等.研究表明,可视图法可为交通流时间序列映射到网络提供有效途径,并且不同状态下交通流时间序列构建的复杂网络的模块化、聚类系数和度分布等统计特征呈现一定的变化规律,为交通流运行态势的研究提供了可视化的分析角度.     

Power-law distribution of gene expression fluctuations

Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.     

Statistical distribution of Chinese names

This paper studies the statistical characteristics of Chinese surnames, first names and full names based on a credible sample. The distribution of Chinese surnames, unlike that in any other countries, shows an exponential pattern in the top part and a power-law pattern in the tail part. The distributions of Chinese first names and full names have the characteristics of a power law with different exponents. Finally, the interrelation of the first name and the surname is demonstrated by using a computer simulation and an exhibition of the name network. Chinese people take the surname into account when they choose a first name for somebody.     

Sales distribution of consumer electronics

Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur quite often. The underlying sales dynamics found between both periods nicely matched a multiplicative process. However, even though the multiplicative term in the process displays a size-dependent relationship when a steady lognormal distribution holds, it shows a size-independent relationship when the power-law distribution holds. This difference in the underlying dynamics is responsible for the difference in the two observed distributions.     

Distribution of Chinese names

We present a statistical model for the distribution of Chinese names. Both family names and given names are studied on the same basis. With naive expectation, the distribution of family names can be very different from that of given names. One is affected mostly by genealogy, while the other can be dominated by cultural effects. However, we find that both distributions can be well described by the same model. Various scaling behaviors can be understood as a result of stochastic processes. The exponents of different power-law distributions are controlled by a single parameter. We also comment on the significance of full-name repetition in Chinese population.     

星-地下行传输孔径接收闪烁频谱的理论和实验研究

基于孔径接收的对数振幅相关函数,结合星地激光下行链路的实际情况,推导了星地下行孔径接收的闪烁频谱表达式。分析了天线孔径和天顶角对闪烁频谱的影响。通过恒星观测实验,对下行孔径接收的闪烁频谱进行了实际测量。实验结果验证了理论计算。研究表明,下行孔径接收的闪烁频谱分为低频段和高频段两部分。低频谱为常量,高频谱呈指数关系变化,指数下降因子为(-11/3)。随着接收孔径尺度增加或天顶角减小,频谱幅值逐渐减小,但闪烁频谱的形状保持不变。     

Scale-free statistics of time interval between successive earthquakes

The statistical property of the calm times, i.e., time intervals between successive earthquakes with arbitrary values of magnitude, is studied by analyzing the seismic time series data in California and Japan. It is found that the calm times obey the Zipf–Mandelbrot power law, exhibiting a new scale-free nature of the earthquake phenomenon. Dependence of the exponent of the power-law distribution on threshold for magnitude is examined. As threshold increases, the tail of the distribution tends to become longer, showing difficulty in statistically estimating time intervals of earthquakes.