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Statistical physics of human behavior
Human behavior with a high degree of complexity. Laws of human behavior, in economics, sociology, research and application management has a very important value. For a long time, the study of human social behavior is mainly psychological interest, by means of experimental psychology, the study of human psychological reactions in a variety of environments is the main means of research. In recent decades, people have made remarkable achievements in the field of complex systems. The study of complex natural systems with the comprehensive and cross-cutting, issue it covers virtually every area of the vast majority of people studied, not only including physics, biology and other natural sciences, including economics, sociology and other social sciences. With the deepening of the study of complex systems, research in the field of penetration of various social disciplines more and more intense, its theoretical and practical applications affecting more and more widely. In recent years, the statistical study of human behavior has become an important issue in complex systems. Unlike traditional methods of psychological experiments, researchers study complex systems for human behavior, mainly through statistical physics methods: by a large number of incidents of human behavior quantitative statistics, statistical study of the hidden laws which, according to the study the problem, the basic assumptions, theoretical model, to explore the mechanism of these laws and the possible impact dynamics. Based on this methodology, it was found that in recent years a large number of special phenomena and laws of human behavior in the presence of these findings sparked the craze for deeper exploration of human social behavior. Especially from 2005 since, only in Nature, Science, PNAS , PRL on strong impact factor journals have been published more than thirty articles.
1 , empirical research time statistical characteristics of human behavior
In a number of previous studies on the socio-economic system, often reduced to a single person's behavior can be used Stationary Random Poisson process described above. This assumption will inevitably lead to the inference is time statistical characteristics of human behavior should be relatively uniform, there is a great probability is very small time interval between two successive acts. However, since 2005 since the actual statistics through time to send and reply human behavior, such as e-mail e-mail communication interval, it was discovered that the presence of these behaviors with the above assumptions very different characteristics [1,2] : long and silent high frequency of outbreaks in the short term, while present in these human behavior, which is inversely proportional to the time distribution that satisfies the power function of the fat tail, that is to say, occurred during these acts can not be described by a Poisson process. The surprising findings suggests that people, individual human behavior may be present complex dynamic mechanism, and an important issue followed by this non-Poisson characteristic in human behavior is not widespread? It is extremely extensive research on this issue was.
Through a variety of data collection methods, one study involving market transactions [3,4,5,6] , web browsing [7,8] , movies on demand [9] , enjoy online music [10] , mobile communications [11 ] behavior in games and virtual communities [12,13] , using the behavior of computer instructions [14] and so on, including commercial activities, entertainment behavior, daily habits and many other human behavior, these behaviors are generally found deviation from Poisson process similar characteristics. These phenomena show, in addition to part of the behavior is strongly influenced by the menstrual cycle, time interval non-Poisson statistics may show characteristics are prevalent in human behavior.
In addition to the distribution of time intervals, the relevant part of human behavior before and after the event interval has also been the attention of researchers. The study found that the relevance of these adjacent interval of human behavior is not obvious, but there are also other explosive silent and long-term nature of natural phenomena (such as earthquakes, etc.) often there is a positive correlation [15] . This is a preliminary study of human behavior and the behavior characteristics of other complex systems were compared, suggesting the existence of mechanisms underlying unity possible.
2 , the study of human behavior dynamics model
The above description of many statistical properties of human behavior can not be used to describe a Poisson process, then an important question is: What is the source of this behavior characteristics of fat tail distribution is? The current interpretation is based on an important task queue theory [1,16,17,18] , it is the people's daily behavior considered to deal with a range of various tasks and assumptions based on experience of everyday life for these tasks to be processed prioritize, first of all deal with high priority ones, have pointed out that this behavior is an important priority cause fat tail distribution. This could reasonably explain the theoretical model of the task queue based on non-Poisson many features of human behavior, such as sending e-mail and surface mail, etc., and can be quite easily extended to the presence of multiple interactions between individuals [ 19] , we have achieved great success in explaining human behavior time statistical distribution of fat tail.
In addition, due to the complexity of human behavior, factors that influence human behavior are diverse, so there are some studies from the viewpoint different from the task queue, we made a variety of non-queuing theory models. For example, some consider working memory effects in human behavior [20] , some to study the effects of cyclical and seasonal behavior of non-Poisson mechanisms [21] , a theory from the recent multiple Poisson distribution It explained the characteristics of human behavior [22] .
Finally, there is the work of a few international non-Poisson studied the characteristics of human behavior impact on the dynamics of network communication, communication, etc. For example, it found that compared to the general transmission characteristics poises, such non-Poisson characteristics may bring some special properties of the system, such as faster speed of propagation [23] . Since this area of development time is very short, there are vast amounts of research work on this issue wait.
3 study, the statistical characteristics of human behavior space
In addition to finding time distribution of human behavior in widespread non-Poisson properties recently discovered there in the spatial distribution of human behavior in complex phenomena non-Poisson characteristics. 2006 years passed through statistical billing [24] , it is indirectly found that the presence of human travel itinerary distribution close to the power law fat tail; 2008 years, Gonzalez and other statistical roaming mobile phone users in different areas of the base station [25] , further study of the distribution of people's travel itinerary, also found that the distribution of scale-free characteristics, consistent with earlier results. Based on more direct GPS statistical conclusions data [26] also support the scale-free distribution of human existence trip. Further, in the biological observation also found that a large number of animal species have similar motion of the stroke of the power-law distribution [27 , 28 , 29] . Due to this higher frequency remote movement of a power-law distribution of travel, it can not be described by classical random walk. This extensive travel distribution, so people need to think about what the dynamic mechanism behind it yes. Although the stroke animal behavior for the power-law distribution have been proposed to optimize the efficiency of feeding [30, 31] , gradient olfactory mechanism [32] , deterministic walking [33]Wait. Current research on the mechanism of this distribution model of the human stroke interpretation is still blank. On the other hand, due to the characteristics of such non-Poisson system often makes the emergence of a number of special properties, then the non-Poisson properties on the spatial distribution of this human behavior is also likely to affect urban traffic, crowd control, the emergency systems operation, could make it with several special nature of these problems has not yet been studied, but also worthy of the attention of researchers.
4 , human behavior dynamics impact on the spread of
Characteristics of human behavior, not only to help people better understand their own behavioral characteristics, to further tap behind these statistics are hidden human characteristics, but also related to the modeling and understanding of people in multiple directions, which most discussed, should be human kinetic impact on the spread of disease in the population. Here mainly from two directions of time and space on the impact of human behavior for speed transmission, spread of range of prevention strategies like.
The classic model of disease transmission, are based on certain assumptions contrary to real human behavior: 1 , the same interval of time human activity, that is all uniform primary, where the "active" activity at each time step, refers to the spread or rehabilitation of behavior; 2 , all of the frequency of activity is no difference in the population, that is, as the density of each individual activity. However, the reference time interval earlier human empirical Statistics found that these assumptions have paroxysmal and human behavior, memory and activity have great access.
Concern for human activities paroxysmal Virus Spread, V á zquez et al check it with E-mail two sets of data, respectively 3188 sent between the users 129 135 messages, 1,729,165 send each user between of 39.04603 million messages, empirical data on the network, based on real time interval, the computer simulates the propagation of viruses on a network [43] . Days and hours, units of statistical results, indicate that the time interval of human behavior meet the power-law distribution, will slow the spread of the virus to a great extent. Paroxysmal human activities have a significant effect on the delay spread of the virus.
Literature [44] also use the SIR model through simulation, the effects of paroxysmal time distribution for the communication process, the model is set up there is waiting time, and the conclusion: the stronger the heterogeneity of time, the probability of survival of the virus small.
Human activity time interval satisfies paroxysmal base memory to investigate the effect of propagation time series process, Karsai et al empirical data based on the telephone network, the time span . 9 months, the size of N = 4.6 × 106 model the propagation of the network [45] . By comparing whether the network containing heavy weights, if there is to network, talk time distribution if there is memory, the simulation results show that a certain degree of heterogeneity will be on human behavior time and space to slow down the communication process.
Time and heterogeneity is reflected in the individual and group level two, there was further compared the effects of both the speed of the spread of the disease [46] . Time-called heterogeneous population level, refers to the time sequence of each person's activity, the average interval, and the frequency are very different between people, to meet the power-law distribution, and individual-level heterogeneity of time, human performance and the same frequency between human activity, and the single active time interval satisfies power-law distribution. Effects of heterogeneity time of propagation velocity on the group level is very large, in contrast, the impact on the spread on the individual level is small.
To reveal the distribution of human influence on the stroke of the propagation process, of Ni et al., Using a probability proportional to the degree of connection, the Euclidean distance is inversely proportional to the mechanism, the network configuration, and network simulation on propagation [47] . The study found that the more distinctive geometric characteristics of travel distribution, that is, people are more inclined to go to the Euclidean distance himself from the more recent places, the smaller the spread of the virus spread to the scope , duration is shorter.
Activity features compared to the individual form of distribution, more people are concerned, in the macro sense, the human impact on the long-range travel between the spread of the virus in the city. As early as 2004 Nian, Hufnagel and others on the aviation network in the United States, assuming a random distribution of population density, established SARS model of virus transmission [48] . The model takes into account the local spread of the virus, and due to the spread of the virus causing the flight of two factors, the results of simulated and empirical good agreement between the city and proposes strategies to effectively prevent and suppress the spread of disease. For the above simulation and analytical results, Hufnagel , who also put forward the corresponding prevention strategies, through simulation, compared reduce individual exposure in some areas and reducing long-range travel-mentioned preventive measures, drawn isolated city, a reduction of long-range travel between cities can more effective prevention of spread of disease, and gives early focus vaccinate remarkable effects [48] . Since then, 2006 Nian Colizza , who carried out a special study on the human impact of long-range travel topology for the spread of the virus caused [49] . To further explore the network topology to influence the distribution of the number of diseases, but also put forward the concept of entropy distribution of the virus, the virus used to portray the popular heterogeneity of the region. By comparison with the case of the actual network transmission of the virus, previously found to characterize many topology model of the human stroke should be improved in detail.
5 , domestic research progress
The rise in this area also attracted the attention of domestic researchers. Currently, the complex systems research group, University of Science and Technology of China, Shanghai Polytechnic University School of Management, Department of Automation, Shanghai Jiaotong University has been so relevant research papers published in academic journals at home and abroad. The work can be summarized as follows:
In empirical terms, complex systems research group of University of Science and Technology of China Zhou Tao et al and Sungkyunkwan University and the Swedish Royal Academy of collaborative research of human behavior on-demand movies and the relationship between the individual and the activity of [9, 34] , Hong Wei and other studies of human time short message communications interval distribution [35] found a variety of scale-free property; Shanghai University of e-mail discussion group of Zhang Ning, Zhou Tao Li Nannan and cooperation analyzes Lu Xun, Qian and other celebrities communication data [36, 37] ; Hu Haibo such as Shanghai Jiaotong University who studied the behavior of the network to listen to music online . [10] in the theoretical model, the Chinese University of Science and technology Han Xiaopu interest and other mechanisms proposed to explain the human adaptive non-Poisson characteristic behavior [38, 39]. in addition, the University of Shanghai for Science and the Chinese side also published a review of human dynamics for [40] , Guo Jinli and so on Shanghai Polytechnic University and the University of Science and technology of China Zhou Tao, who co-authored the publication "kinetic model of human behavior," a monograph [41] , University of Science and technology of China Zhou Tao, Han Xiaopu, Wang Binghong also a world Science Agency published the monograph " : Science Matters Humanities Complex Systems AS in" wrote a special chapter on the study of human dynamics [42] .
6 , the main problem facing
Due to the development in the field of short time, there is at present in-depth study of a large number of issues need to be:
First, the existing empirical statistics aimed at individual behavior, but there are still a large number of individual behavior characteristic has not been studied existing research results is still difficult to distinguish the main categories based on the statistical characteristics of individual behavior; and positive behavior for groups more research is almost blank. In fact, human behavior often suffer from the effects of social relations, quantitative empirical research in this area is still very lacking. In addition, some recent theories of development, such as human dynamics universality class hypothesis has been challenged by new empirical data, a clearer and more convincing picture of needs and more in-depth empirical analysis.
Second, in addition to individual human behavior, some of the latest statistics we do have found that some social groups have similar macroscopic behavior of non-Poisson characteristics, such as the distribution of time intervals between wars and other countries; due to the current limited empirical statistics, social groups, these characteristics in memory, whether the individual human behavior has a similar mechanism of generation, are still unknown issue, the need for in-depth study to what extent.
Third, in terms of the spatial distribution of human behavior, the current empirical data based on all bills, mobile phone roaming data indirectly, the lack of direct observation of human behavior spatial distribution; and its production mechanism and kinetic aspects of the effects of There is little research.
Fourth, the current study theoretical models, although several have been proposed phase-only mechanism to explain human behavior in non-Poisson characteristics, but these mechanisms is difficult to cover all non-Poisson characteristics of the phenomenon of human behavior, the need for new and more It has proposed a universal model.
Fifth, the effects of human behavioral characteristics of dynamic effects of various social systems, although there have been few studies in this area, but many issues involved, particularly research gaps, needs a lot of work intensified. For example, the spatial distribution characteristics of human behavior that affect urban transport.
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