基于随机矩阵理论的城市人群移动行为分析

移动通信应用为人类移动规律的研究提供了独特的数据来源. 本文通过城市手机用户的分布数据,研究城市移动人群的整体动力学行为. 借助随机矩阵理论的方法,通过比较移动人群数据与随机数据在互相关矩阵谱分布上的差异,发现移动人群数据互相关矩阵的相关系数均值、最大本征值及其对应的本征向量明显偏离于随机互相关矩阵的分布,指出这种差异体现了城市移动人群的整体行为特性,且这种差异在不同时间段也会有所不同. 研究结果体现出相关系数的均值和最大本征值的波动趋势,并指出本征向量成员权重的时空模式与城市移动人群整体行为特征的波动过 关键词： 随机矩阵理论 移动人群 宏观行为     

Insights into a spatially embedded social network from a large-scale snowball sample

Much research has been conducted to obtain insights into the basic laws governing human travel behaviour. While the traditional travel survey has been for a long time the main source of travel data, recent approaches to use GPS data, mobile phone data, or the circulation of bank notes as a proxy for human travel behaviour are promising. The present study proposes a further source of such proxy-data: the social network. We collect data using an innovative snowball sampling technique to obtain details on the structure of a leisure-contacts network. We analyse the network with respect to its topology, the individuals’ characteristics, and its spatial structure. We further show that a multiplication of the functions describing the spatial distribution of leisure contacts and the frequency of physical contacts results in a trip distribution that is consistent with data from the Swiss travel survey.     

The scaling of human mobility by taxis is exponential

As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users’ locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis’ traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.     

Spatiotemporal Patterns of Urban Human Mobility

The modeling of human mobility is adopting new directions due to the increasing availability of big data sources from human activity. These sources enclose digital information about daily visited locations of a large number of individuals. Examples of these data include: mobile phone calls, credit card transactions, bank notes dispersal, check-ins in internet applications, among several others. In this study, we consider the data obtained from smart subway fare card transactions to characterize and model urban mobility patterns. We present a simple mobility model for predicting peoples’ visited locations using the popularity of places in the city as an interaction parameter between different individuals. This ingredient is sufficient to reproduce several characteristics of the observed travel behavior such as: the number of trips between different locations in the city, the exploration of new places and the frequency of individual visits of a particular location. Moreover, we indicate the limitations of the proposed model and discuss open questions in the current state of the art statistical models of human mobility.     

Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost∕benefit model

Probability distributions of human displacements have been fit with exponentially truncated Le?vy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2, and (>) 3. These three exponents correspond to three displacement range zones of about 1 km ?Δr?10 km, 10 km ?Δr?300 km, and 300 km ?Δr?1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost∕benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium, and far distances) and would assume that the travel benefits are randomly∕uniformly distributed mostly only within specific urban-like areas. The three displacement distribution zones appear to be characterized by an integer (1, 2, or >3) inverse power exponent because of the specific number (1, 2, or >3) of cost mechanisms (each of which is proportional to the displacement length). The distributions in the first two zones would be associated to Pareto distributions with exponent β?=?1 and β?=?2 because of simple geometrical statistical considerations due to the a priori assumption that most benefits are searched in the urban area of the city of residence or in the urban area of specific nearby cities. We also show, by using independent records of human mobility, that the proposed model predicts the statistical properties of human mobility below 1 km ranges, where people just walk. In the latter case, the threshold between zone 1 and zone 2 may be around 100-200 m and, perhaps, may have been evolutionary determined by the natural human high resolution visual range, which characterizes an area of interest where the benefits are assumed to be randomly and uniformly distributed. This rich and suggestive interpretation of human mobility may characterize other complex random walk phenomena that may also be described by a N-piece fit Pareto distributions with increasing integer exponents. This study also suggests that distribution functions used to fit experimental probability distributions must be carefully chosen for not improperly obscuring the physics underlying a phenomenon.     

基于手机大数据的中国人口迁徙模式及疫情影响研究

新型冠状病毒感染的肺炎(COVID-19)可通过人员接触与流动迅速传播,因此研究人类迁徙和出行模式的变化对疫情防控至关重要.本文基于手机运营商2020年春运及疫情暴发前后连续两个月的全国地级市之间的人口流动数据,运用时序网络分析方法构建人口流动网络拓扑结构指标,并通过引入地理衰减因子提出Spatial-Louvain社团检测算法,研究平时、春运、疫情防控隔离和生产复工四阶段的人口迁徙模式的时空演化规律.研究发现:受各地疫情防控措施影响,武汉封城后全国城市间人口流量急剧下降,并持续至2月中旬.疫情期间人口流动网络结构呈现四阶段的时空演化模式;本文提出的空间网络社团检测算法比传统Louvain算法平均模块度值提高了14%;中国城市分布以经济交互和地理位置为基础,形成了以核心城市为中心,向周边辐射的城市群格局;疫情因素仅能在短暂时间内改变部分城市的城市群归属,当该因素消失或减弱后,城市群能迅速恢复原有格局.     

Exploring the mobility of mobile phone users

Mobile phone datasets allow for the analysis of human behavior on an unprecedented scale. The social network, temporal dynamics and mobile behavior of mobile phone users have often been analyzed independently from each other using mobile phone datasets. In this article, we explore the connections between various features of human behavior extracted from a large mobile phone dataset. Our observations are based on the analysis of communication data of 100,000 anonymized and randomly chosen individuals in a dataset of communications in Portugal. We show that clustering and principal component analysis allow for a significant dimension reduction with limited loss of information. The most important features are related to geographical location. In particular, we observe that most people spend most of their time at only a few locations. With the help of clustering methods, we then robustly identify home and office locations and compare the results with official census data. Finally, we analyze the geographic spread of users’ frequent locations and show that commuting distances can be reasonably well explained by a gravity model.     

Dynamical behaviour of an epidemic on complex networks with population mobility

In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population's mobility on the epidemic spreading. In view of the population's mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.     

天山北坡绿洲城市车流量与对流层NO2垂直柱浓度关系研究

为探讨天山北坡河谷绿洲城市车流量与对流层NO₂垂直柱浓度(VCD)的关系,基于各城市车流量状况,利用地基多轴差分光谱仪(Mini MAX-DOAS)在2018年—2019年天山北坡经济带上的综合性大城市乌鲁木齐、工业型中等城市石河子和工业型小城市阜康市中心区连续固定监测,并沿城市交通主干道进行车载移动监测,研究车流量对NO₂VCD的影响,对比分析山盆体系河谷绿洲城市与中东部发达城市污染严重原因的差异。结果表明:(1)天山北坡大中小城市的车流量日均值大城市乌鲁木齐(1 406辆/5 min)远大于中小城市,中等城市石河子(203辆/5 min)和小城市阜康(185辆/5 min)差异并不显著(p>0.05),而各类城市NO₂VCD整体差异显著(p<0.05),其日变化峰值有所差异,表现为乌鲁木齐(22.613×10¹⁵ molec·cm^-2)>阜康(17.758×10¹⁵ molec·cm^-2)>石河子(15.2...     

Effects of urban morphology on the traffic noise distribution through noise mapping: A comparative study between UK and China

Due to the rapid urban development and massive population increase in many eastern cities, the difference in urban density and morphology between typical western and eastern cities is becoming significant. This consequently makes the noise distribution in the eastern cities rather different from typical low density European cities. In this research, two representative cities with different urban densities, Greater Manchester in the UK and Wuhan in China, were selected, which have low and high average urban density respectively, and also have considerable differences in building form and traffic pattern. In the mean time, these two cities have similar urban scale and traffic amount. In each city, based on the urban morphological analyses considering urban land-use, building and road density, and noise source distribution, a number of typical urban areas, 500 * 500 m² each, were sampled. A noise-mapping software package was then used to generate generic noise maps, based on existing digital vector maps for terrain and building, and traffic data obtained by on-site measurements. The comparison results show that the average and minimum noise level in Greater Manchester samples is generally higher than that in Wuhan samples, while the maximum noise level in Wuhan samples is mostly higher. By developing a Matlab program, correlations have been analysed between noise distributions and the urban characteristics relating to urban density, such as the road and building coverage ratio. Overall, comparisons between these two typical cities have shown significant effects of urban morphology on the traffic noise distribution.     

Exploring space-time structure of human mobility in urban space

Understanding of human mobility in urban space benefits the planning and provision of municipal facilities and services. Due to the high penetration of cell phones, mobile cellular networks provide information for urban dynamics with a large spatial extent and continuous temporal coverage in comparison with traditional approaches. The original data investigated in this paper were collected by cellular networks in a southern city of China, recording the population distribution by dividing the city into thousands of pixels. The space-time structure of urban dynamics is explored by applying Principal Component Analysis (PCA) to the original data, from temporal and spatial perspectives between which there is a dual relation. Based on the results of the analysis, we have discovered four underlying rules of urban dynamics: low intrinsic dimensionality, three categories of common patterns, dominance of periodic trends, and temporal stability. It implies that the space-time structure can be captured well by remarkably few temporal or spatial predictable periodic patterns, and the structure unearthed by PCA evolves stably over time. All these features play a critical role in the applications of forecasting and anomaly detection.     

The mathematical relationship between Zipf’s law and the hierarchical scaling law

The empirical studies of city-size distribution show that Zipf’s law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf’s distribution of cities is abstracted as a q$q$-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf’s law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2ⁿ$2^n$ principle and Pareto’s law can be associated with one another by the hierarchical organization.     

The backbone of a city

Recent studies have revealed the importance of centrality measures to analyze various spatial factors affecting human life in cities. Here we show how it is possible to extract the backbone of a city by deriving spanning trees based on edge betweenness and edge information. By using as sample cases the cities of Bologna and San Francisco, we show how the obtained trees are radically different from those based on edge lengths, and allow an extended comprehension of the “skeleton” of most important routes that so much affects pedestrian/vehicular flows, retail commerce vitality, land-use separation, urban crime and collective dynamical behaviours.     

Centrality in networks of urban streets

Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structure, nicely capturing the skeleton of most central routes and subareas that so much impacts on spatial cognition and on collective dynamical behaviors. Statistically, closeness, straightness and betweenness turn out to follow similar functional distribution in all cases, despite the extreme diversity of the considered cities. Conversely, information is found to be exponential in planned cities and to follow a power-law scaling in self-organized cities. Hierarchical clustering analysis, based either on the Gini coefficients of the centrality distributions, or on the correlation between different centrality measures, is able to characterize classes of cities.     

Recurrent host mobility in spatial epidemics: beyond reaction-diffusion

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modeled by diffusion in space or on metapolulation networks. Alternatively, an effective force of infection across distance has been introduced to capture spatial dispersal implicitly. Both approaches do not account for important aspects of natural human mobility, diffusion does not capture the high degree of predictability in natural human mobility patters, e.g. the high percentage of return movements to individuals’ base location, the effective force of infection approach assumes immediate equilibrium with respect to dispersal. These conditions are typically not met in natural scenarios. We investigate an epidemiological model that explicitly captures natural individual mobility patterns. We systematically investigate generic dynamical features of the model on regular lattices as well as metapopulation networks and show that generally the model exhibits significant dynamical differences in comparison to ordinary diffusion and effective force of infection models. For instance, the natural human mobility model exhibits a saturation of wave front speeds and a novel type of invasion threshold that is a function of the return rate in mobility patterns. In the light of these new findings and with the availability of precise and pervasive data on human mobility our approach provides a framework for a more sophisticated modeling of spatial disease dynamics.     

Why are large cities faster? Universal scaling and self-similarity in urban organization and dynamics

Cities have existed since the beginning of civilization and have always been intimately connected with humanity's cultural and technological development. Much about the human and social dynamics that takes place is cities is intuitively recognizable across time, space and culture; yet we still do not have a clear cut answer as to why cities exist or to what factors are critical to make them thrive or collapse. Here, we construct an extensive quantitative characterization of the variation of many urban indicators with city size, using large data sets for American, European and Chinese cities. We show that social and economic quantities, characterizing the creation of wealth and new ideas, show increasing returns to population scale, which appear quantitatively as a power law of city size with an exponent β≃ 1.15 > 1. Concurrently, quantities characterizing material infrastructure typically show economies of scale, namely β≃ 0.8 < 1. The existence of pervasive scaling relations across city size suggests a universal social dynamics common to all cities within an urban system. We sketch some of their general ingredients, which include the acceleration of social life and a restructuring of individual social networks as cities grow larger. We also build simple dynamical models to show that increasing returns in wealth and innovation can fuel faster than exponential growth, which inexorably lead to crises of urban organization. To avoid them we show that growth may proceed in cycles, separated by major urban adaptations, with the unintended consequence that the duration of such cycles decreases with larger urban population size and is now estimated to be shorter than a human lifetime.     

手机通话网络度特征分析

手机通信数据详细记录了人们的通信行为, 成为研究人们社会关系、行为模式的重要资源. 通话号码个数、通话次数和时长是手机通信网络的基本属性. 本文在复杂网络理论基础上, 应用统计的方法研究了中国西部某城市三百余万手机用户不同节假日和工作日的 四天通话数据在不同尺度下的号码度、通话度、时长度的分布以及平均号码度、 平均通话度、平均时长度的特征.研究表明, 所有尺度下, 号码度、通话度、时长度均为幂律分布, 幂指数随尺度、日期和指标的不同而不同, 在[1.3, 4] 范围内波动.总体上, 号码度幂指数大于通话度和时长度幂指数, 入度幂指数大于出度幂指数;节假日幂指数大于相应指标的工作日幂指数, 休息时段幂指数大于工作时段幂指数;与工作日相比, 节假日的平均号码度和平均通话度较小, 平均时长度较大.揭示了绝大多数用户每日只接打1个号码的电话, 节假日期间接打电话的用户数、次数、时长减少, 但平均通话时长增大的特征. 关键词： 手机通话网络 复杂网络 度分布 通话模式     

Diffusive Resettlement: Irreversible Urban Transitions in Closed Systems

We propose a non-equilibrium framework for modelling the evolution of cities, which describes intra-urban migration as an irreversible diffusive process. We validate this framework using the actual migration data for the Australian capital cities. With respect to the residential relocation, the population is shown to be composed of two distinct groups, exhibiting different relocation frequencies. In the context of the developed framework, these groups can be interpreted as two components of a binary fluid mixture, each with its own diffusive relaxation time. Using this approach, we obtain long-term predictions of the cities’ spatial structures, which define their equilibrium population distribution.     

基于车载多轴差分吸收光谱技术对城市NO2污染分布和排放评估研究

二氧化氮（NO₂）在大气光化学中发挥着重要作用,不仅参与了对流层臭氧（O₃）的催化生成,同时也能促进生成二次气溶胶。NO₂作为交通运输和工业过程中的重要排放产物,通常也被视为一种评估人为污染源排放的指示物,因此,开展城市NO₂分布与排放研究对于城市大气污染管控与治理具有重要意义。2018年1月和2月期间,基于车载多轴差分吸收光谱技术（MAX-DOAS）对衡水市区开展了4次走航观测实验,获取了衡水市区环城路上对流层NO₂垂直柱浓度（VCD）的空间分布,其浓度范围为0.89×1015~56.33×1015 molecule·cm-2,均值在22.42×1015~30.20×1015 molecule·cm-2。观测结果表明衡水市NO₂污染源主要分布在城外东南方向的工业聚集区,以及市区环城路东部的立交桥路段;而城市西部和北部则较为干净,当风场来自该区域会对污染源区起到一定的清洁作用,可使源区NO₂浓度降低20%以上。航测期间进行了站点对比观测,综合两者的观测结果评估了衡水市东部污染区域的相对贡献,其NO₂含量比西部洁净区域高出了30.1%~61.9%、贡献值高7.89×1015~13.32×1015 molecule·cm-2。将NO₂城市分布与WRF模式模拟的气象数据相结合,可计算出目标区域的NO₂本地排放通量为0.86×1024 molecule·s-1,该结果相对较低,一方面说明衡水市区相对于其他研究区域,其NO₂污染源并非在集中在市区内部;另一方面是因为本次实验研究区域的面积仅有50 km2,远小于其他研究的城市区域范围。对于实验测得的衡水市区输出总通量,其中96.16%来源于外部传输,3.84%为本地排放造成,进一步证明了衡水市NO₂主要污染源位于城外。通过实验期间衡水市区的后向轨迹气团与OMI卫星的NO₂平均结果可看出,衡水市除城市东部和东南部的本地污染源外,也受到了北部的保定、廊坊和西北部的石家庄等地的污染传输影响。总体来看,车载多轴差分吸收光谱技术对于城市NO₂等污染气体的源区确认、污染贡献评估和排放通量计算方面有较出色的应用前景。     

A model of peasant labor in China

Nowadays in the rural areas of China, peasants can make their own choices to go to the city for a new job or stay in the rural area. A decision is made based on working ability and the information a peasant gets. A multivariate evolutionary model of this problem is established and the numerical simulation shows that going to the city brings about a rise in the peasants’ income, and also that such a rise, as well as the number of peasants going to the city, is influenced by the capacity of the cities and income gap between agricultural and non-agricultural industries.