Empirical analysis on temporal statistics of human correspondence patterns

Recently, extensive empirical evidence shows that the timing of human behaviors obeys non-Possion statistics with heavy-tailed interevent time distribution. In this paper, we empirically study the correspondence pattern of a great Chinese scientist, named Hsue-Shen Tsien. Both the interevent time distribution and response time distributions deviate from the Poisson statistics, showing an approximate power-law decaying. The two power-law exponents are more or less the same (about 2.1), which strongly support the hypothesis in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127] that the response time distribution of the tasks could in fact drive the interevent time distribution, and both the two distributions should decay with the same exponent. Our result is against the claim in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127], which suggests the human correspondence pattern belongs to a universality class with exponent 1.5.     

Human comment dynamics in on-line social systems

Human comment is studied using data from ‘tianya’ which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some “hubs” in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.     

Individual and group dynamics in purchasing activity

As a major part of the daily operation in an enterprise, purchasing frequency is in constant change. Recent approaches on the human dynamics can provide some new insights into the economic behavior of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plots. It’s found that the former displays a power-law distribution with approximate exponent 2.0, while the latter is fitted by a mixture distribution with both power-law and exponential characteristics. Obviously, two distinctive characteristics are presented for the interval time distribution from the perspective of individual dynamics and group dynamics. Actually, this mixing feature can be attributed to the fitting deviations as they are negligible for individual dynamics, but those of different vendors are cumulated and then lead to an exponential factor for group dynamics. To better describe the mechanism generating the heterogeneity of the purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good agreement with the empirical data.     

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.     

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

人类行为的动力学与统计力学研究

对人类行为的统计特性的研究,涉及研究经济、心理、交通、社会学等学科的根本问题.在最近一个时期以来,针对人类行为的统计揭示出了大量的出乎人们意料的规律,吸引了众多研究者的注意.这些规律不仅对认识人类自身和对大量的社会学科的基础研究有着重要价值,而且在实际应用中有着广阔的前景.文章作者回顾了这一新近发展起来的领域的主要研究成果,并重点对中国科学技术大学的相关研究进行了介绍.     

人类行为的动力学与统计力学研究

对人类行为的统计特性的研究,涉及研究经济、心理、交通、社会学等学科的根本问题.在最近一个时期以来,针对人类行为的统计揭示出了大量的出乎人们意料的规律,吸引了众多研究者的注意.这些规律不仅对认识人类自身和对大量的社会学科的基础研究有着重要价值,而且在实际应用中有着广阔的前景.文章作者回顾了这一新近发展起来的领域的主要研究成果,并重点对中国科学技术大学的相关研究进行了介绍.     

Fractal analysis on human dynamics of library loans

In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.     

在线协同写作的人类动力学分析

对人类在线行为模式的探讨是近年来人类动力学研究的热点.基于维基百科数据,文章针对一类重要且普遍的在线行为--在线协同写作,进行时间统计特性分析和内容更新统计分析.实证显示在线协同写作时间间隔分布呈多尺度特征,1 min到30 min和30 min到24 h两个时间段上时间间隔分别服从指数为1.62和1.16的幂律分布,而大于24 h的时间间隔服从形如F(τ)∝τ^{－b－alog(τ)}的累积分布.分析表明 关键词： 在线协同写作 人类动力学 多尺度特征 维基百科     

Heterogenous scaling in the inter-event time of on-line bookmarking

In this paper, we study the statistical properties of bookmarking behaviors in Delicious.com. We find that the inter-event time (τ) distributions of bookmarking decay in a power-like manner as τ increases at both individual and population levels. Remarkably, we observe a significant change in the exponent when the inter-event time increases from the intra-day range to the inter-day range. In addition, the dependence of the exponent on individual activity is found to be different in the two ranges. Instead of monotonically increasing with activity, the inter-day exponent peaks around 3. These results suggest that the mechanisms driving human actions are different in the intra-day and inter-day ranges. We further show that the global distributions of less active users are closer to an exponential distribution than those of more active users. Moreover, a universal behavior in the inter-day range is observed by considering the rescaled variable τ/〈τ〉. Finally, the possible causes of these phenomena are discussed.     

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.     

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.     

Time-varying human mobility patterns with metapopulation epidemic dynamics

In this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree _kc$k_c$. For nodes with degree smaller than _kc$k_c$, the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than _kc$k_c$, the pattern produces a negative impact on epidemic mitigation.     

Social network based microblog user behavior analysis

The influence of microblog on information transmission is becoming more and more obvious. By characterizing the behavior of following and being followed as out-degree and in-degree respectively, a microblog social network was built in this paper. It was found to have short diameter of connected graph, short average path length and high average clustering coefficient. The distributions of out-degree, in-degree and total number of microblogs posted present power-law characters. The exponent of total number distribution of microblogs is negatively correlated with the degree of each user. With the increase of degree, the exponent decreases much slower. Based on empirical analysis, we proposed a social network based human dynamics model in this paper, and pointed out that inducing drive and spontaneous drive lead to the behavior of posting microblogs. The simulation results of our model match well with practical situation.     

在线热点事件的时空演变规律

为了理解舆论的时空演变斑图并揭示其形成机理, 本文运用统计物理学方法, 通过对在线评论数据进行统计分析, 定量地研究了在线热点事件关注度(在线评论数) 的时空演变规律. 实证表明, 虽然事件关注度在不同地区的分布存在极大的异质性, 即遵循双段幂律分布; 但是不同地区内事件的关注程度在时间演变过程中却表现出明显的一致性, 其不同时间内的Zipf分布变化很小. 关联性分析显示地区关注度受到该地区经济的显著影响, 而不同地区关注度演变行为的一致性来源于地区之间的强关联性. 另一方面, 舆论引导将显著影响事件的关注度, 导致传播速度(单位时间内评论数的增量) 急剧增加. 通过计算不同地区传播速度的信息熵, 我们发现评论的地区分布在大部分时间内都具有一致性, 而舆论引导有助于保持这种一致性. 地区传播速度之间的关联性分析表明在整个事件中经济较发达地区的舆论变化更趋于一致, 暗示这些地区对于舆论引导的响应更快, 因此加强发达地区的舆论引导有利于控制舆论的整体传播.     

Entropy analysis of the dynamics of El Niño/Southern Oscillation during the Holocene

This study explores temporal changes in the dynamics of the Holocene ENSO proxy record of the Laguna Pallcacocha sedimentary data using two entropy quantifiers. In particular, we analyze the possible connections between changes in entropy and epochs of rapid climate change (RCC). Our results indicate that the dynamics of the ENSO proxy record during the RCC interval 9000-8000 BP displays very low entropy (high predictability) that is remarkably different from that of the other RCCs of the Holocene. Both entropy quantifiers point out to the existence of cycles with a period close to 2000 years during the mid-to-late Holocene. Within these cycles, we find a tendency for entropy to increase (predictability to decrease) during the two longer RCC periods (6000-5000 and 3500-2500 BP) which might be associated with the reported increased aridity of the low tropics.     

A study of design approach of spreading schemes for viral marketing based on human dynamics

Before launching a real viral marketing campaign, it is needed to design a spreading scheme by simulations. Based on a categorization of spreading patterns in real world and models, we point out that the existing research (especially Yang et al. (2010) Ref.  [16]) implicitly assume that if a user decides to post a received message (is activated), he/she will take the reposting action promptly (Prompt Action After Activation, or PAAA). After a careful analysis on a real dataset however, it is found that the observed time differences between action and activation exhibit a heavy-tailed distribution. A simulation model for heavy-tailed pattern is then proposed and performed. Similarities and differences of spreading processes between the heavy-tailed and PAAA patterns are analyzed. Consequently, a more practical design approach of spreading scheme for viral marketing on QQ platform is proposed. The design approach can be extended and applied to the contexts of non-heavy-tailed pattern, and viral marketing on other instant messaging platforms.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Microscopic information processing and communication in crowd dynamics

Due, perhaps, to the historical division of crowd dynamics research into psychological and engineering approaches, microscopic crowd models have tended toward modelling simple interchangeable particles with an emphasis on the simulation of physical factors. Despite the fact that people have complex (non-panic) behaviours in crowd disasters, important human factors in crowd dynamics such as information discovery and processing, changing goals and communication have not yet been well integrated at the microscopic level. We use our Microscopic Human Factors methodology to fuse a microscopic simulation of these human factors with a popular microscopic crowd model. By tightly integrating human factors with the existing model we can study the effects on the physical domain (movement, force and crowd safety) when human behaviour (information processing and communication) is introduced.In a large-room egress scenario with ample exits, information discovery and processing yields a crowd of non-interchangeable individuals who, despite close proximity, have different goals due to their different beliefs. This crowd heterogeneity leads to complex inter-particle interactions such as jamming transitions in open space; at high crowd energies, we found a freezing by heating effect (reminiscent of the disaster at Central Lenin Stadium in 1982) in which a barrier formation of naïve individuals trying to reach blocked exits prevented knowledgeable ones from exiting. Communication, when introduced, reduced this barrier formation, increasing both exit rates and crowd safety.