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荷兰留学生课程Assignment指导案例：人口流动性的管理研究，流动性指的是人、图像和物体在本地和全球的地理空间中快速移动的能力。流动性和身份的交叉点涉及到如何理解通过移动性的跨空间，运动之间的空间或缺乏空间运动如何导致特征的变化，以及不同的尺寸和类型的流动性如何构造不同的身份概念。流动性具有不同的含义，以及一系列的影响；高层次的空间流动性同时是技术增强的社会现实，日常生活的必要性和许多文化的愿景。
流动性是一个相对稀缺的社会能力，但它是用它的反面来定义的，固定性，当一些事物或人在移动，其他人却在停泊，他们的动作收到了限制或是困难的。不同类型的移动已经成为可能，并且在更大的尺度上发生着，随着各种创新技术的支持，在全球化的时代变得更明，从数字化到远程喷气式飞机。 Mobility refers to the capacity of people, images, and objects to move rapidly across local and global geographic space. The intersection of mobility and identity is concerned with how identity is understood through mobility across spaces, how the movement between spaces or lack of movement between spaces results in identity shifts, and how different dimensions and types of mobility construct different notions of identity. Mobility has diverse meanings as well as a range of implications; high levels of spatial mobility are simultaneously a social fact of technologically enhanced society, a necessity of everyday life and a cultural aspiration of many. Mobility is a relatively scarce social capacity and is defined by its opposite, immobility, for whenever some things or people are mobile, others are moored, their movements restricted or difficult. Mobilities of various types have become more possible, occur on a larger scale, and are more evident in the global era with the assistance of various technological innovations, from digitalization to long-range jet airplanes. As well as informing new theories and accounts of globalization, the field of mobilities research encompasses the study of movements of people, goods, and vehicles locally and within cities, informing developments in and forging alliances with disciplines such as geography and urban planning. Some, such as John Urry, argue that this new focus on mobilities provides a challenge to the traditionally static view of the social world and social or cultural identities in the social sciences. Urry suggests the concept of mobilities should form an overarching conceptual framework for a new era of the social sciences that is post globalization studies, and driven by innovative theorizing in new areas such as network studies, digital technologies, and transportation studies that write in mobility as a core dimension of social life. 移动性——Mobility The concept of mobility brings together human characteristics of identity and power with a dynamic understanding of space, place, and change. Different mobilities are shaped by different geographies, by the varying types of spaces people move through (e.g., public or private, urban or rural, real or virtual), and by a range of factors from cultural norms to modern security and immigration controls. Further influences include access to the means of mobility, be they cars, computers, bikes, or pavements, and the varying ability to be mobile, based on age, sex, body type, and other components of identity. Mobility is constructed in relationship to relative immobility, or what are sometimes termed moorings, locations where mobility appears temporarily abated. Yet as absolute immobility is all but impossible, the mobility concept proposes that everyone and everything is mobile and that it is matters of scale, difference in speed, and variation in direction that create appearances of relative immobilities. Mobility can also be used to assess the impact of modern telecommunication and computer technologies on socio spatial relations, such as changing labour practices through which the mobile office makes almost any location a potential workplace, and, in a more metaphorical context, to explore the virtual experiences of moving through spaces via the Internet, videogames, television, and film. Consequently, where past geographical studies commonly analyzed such places as isolated entities, theories of mobility understand space as interconnected networks through which flows of people, goods, technologies, information, and images move. This constant movement forms the basis for analyses of mobility yet does not deny that there are material aspects to life. Mobility is not ethereal. It is tied to places and exhibited through physical forms. Mobility is relational and differs from person to person. It matters who is doing the moving, where, when, how, and why. Immigrants, Diaspora populations, and international tourists experience mobility differently from commuters, nomadic peoples, or prisoners. Men and women experience moving through space differently, as do young and old, people of different social classes, races, ethnicities, and nationalities. For example, if an adult and a child are travelling together, the child, while involved in the same movement, does not experience the same sense of mobility, and thus, the two individuals understand and practice very different mobilities. Similarly, mobility in contemporary European space is very different for an academic with a British passport going to a conference than it is for an Ethiopian economic migrant moving through the illicit spaces of the underground economy. Encountering difference is often an aspect of mobility. Travel writings and accounts of foreign journeys commonly romanticize unfettered movement through the places of otherness, whereas vacations, exile, and emigration are experiences of difference that generate disparate mobilities. 社会理论中的移动性——Mobility in Sociological Theory Theories of mobility exist at two levels: the factual and the metaphorical. First, they refer to a set of facts describing key facets and characteristics of the contemporary social world associated with globalization, technological changes, fluidities, and speed. These bodies of work argue that the world is characterized by unprecedented levels of mobilities: capital, people, information, and objects are circling the globe more frequently, in greater volume, and with greater speed. Increasingly, as the global reach of economic and cultural interactions intensifies, these things recognize no boundaries. This means that social action must be re-imagined as possibly being able to take place at a distance, and those ideas about home and not-home, local and global, must be substantially rethought. Furthermore, it is not just people that are mobile, but various types of objects, which creates increasingly complex global infrastructural and communications networks. In the digital era, as a result of such things as the Internet, laptop computers, and increasingly sophisticated mobile telephony, parcels of information relating to finance, leisure, trade, and politics all circulate relatively freely across borders. Second, mobility also refers to a set of theoretical metaphors which some argue challenge traditional approaches to describing and analyzing the social world. The new theoretical metaphors of vertigo-inducing flux, mobility, and fast-paced change continue to capture the theoretical spirit of our times. Traditionally, mobility in sociology has been concerned with examining the nature and extent of vertical social mobilities, with mobility referring to a central dimension of class and stratification studies. In this field, mobility measures individuals' capacity to scale the social ladder, according to their relative accumulation of valuable assets such as education and economic capital, and against social structures such as family history, geographic location, and inherited wealth. In this view, people cannot be said to circulate or be fluid in any real sense. Rather, their mobility is theorized within a schematic, spatially bounded, and often quite rigid or slow-moving model of social relationships, where mobility refers to individuals' capacity to gradually alter their accumulation of socially valued assets such as education or income throughout the life course. Against this traditional sense of social mobility, the contemporary metaphor of mobility has been used to describe both a set of epistemological and material shifts that drastically reform the way sociologists might attend to theorizing the basic structures of social and economic life. 移动性的系统管理——Systems That Enable and Govern Mobilities Mobilities are centrally linked to elements of infrastructure that configure and enable the mobilities. Many of these things that enable mobilities are fixed in place and actually immobile, enlisted into an interdependent technological system that supports massive global systems of mobility. For example, systems of global air travel rely on airport hubs such as Singapore or Dubai, strategically located around the globe for ease and scale of distributing passengers to other regional hubs or smaller ports, and that support the capacity of airliners to travel only certain distances without refueling. Global air travel also relies on the existence of fixed radio beacons for navigation, transmissions from a terrestrial radio station for fixing a glide slope to find the runway, or runway lighting to visually alert pilots to the runway upon descent. There are many other examples of such technological infrastructures that facilitate global mobility, including ports, docks, factories, storage areas, garages, and roads.#p#分页标题#e# The increased scale and frequency of mobility means that governments and organizations must increasingly pay attention to potential problems that might arise because of mobile people and things. Mobility becomes a matter of governance-of tracing, mapping, and monitoring things that move about. To continue with the previous example, radar systems monitor the movement of airplanes around the world and dictate various aspects of route such as altitude or bearing so they do not directly encounter other aircraft. Another pertinent example relates to systems of monitoring global population movements. Many authors point to the way globally networked computers and software form the basic infrastructure required for sorting, checking, classifying, and monitoring transnational movements of people through ports and airports, . The material basis for governing this mobility rests in the passport, a document that enables its owner to pass through ports in a recognized and controlled manner, yet consigns others to queues, interview rooms, and international holding zones. 移动性的尺寸和类型——Dimensions and Types of Mobility Two basic aspects that compel human mobility can be distinguished: one based on choice that is elective and capacity-based, and another that is a compulsory or forced mobility based on displacement or dislocation. In the former type, transnational mobility is fast becoming a value in itself, a good news story for people who are caught up in the routines of everyday life that continues to be steeped in the familiar and local. This type of mobility is based on volition, choice, and the capacity of individuals to be mobile in various ways. Here, the promise is of travel, connection, and generally pleasurable contact with distant others and places and of associated enhanced economic opportunities. This type of mobility often relies on forms of social and cultural capital associated with income or occupation. For example, some people are able to be globally mobile in their work because they have high-level or highly sought-after skills, often in fields of business or technology. But, this type of mobility is in turn based on privileged forms of cultural and economic capital, meaning it is not an evenly distributed social capacity. Other people may move because they are employed by transnational corporations such as banks, hotels, or airlines that rely on a globally mobile, skilled labor force at the executive level. Sometimes, however, workers temporarily migrate between countries to fill relatively low-paid occupations in more developed nations, such as nannies or hotel workers. Alternately, some forms of mobility are forced by necessity or situation. This is the case with refugees or political asylum seekers, for example, which may flee oppression, violence, natural disaster, or social breakdown within their home countries. The result of such mobilities is that nation-state boundaries are increasingly porous, with some arguing this represents a significant reorganization of historical global social spaces associated with the nation state. For example, Neil Brenner has argued that global history is characterized by rounds of global restructuring that induces population flows that result in the deterritorialization of some places and the reterritorialization of others. What emerges is that the global population is in constant flux, a tangled mosaic of mobilities at various levels and scales, situated against some stable and strong nation-states trying to stem and control frequent arrivals at their border zones. Three types of mobilities, based on how human mobility is achieved, can also be distinguished. First, are corporeal mobilities, referring to the bodily movements of people. These can be on various scales and for various reasons. For example, within their local geographies, people may travel relatively small distances frequently for food, work, or social contact. Other types of corporeal mobilities are wide reaching, transcontinental, and often for the purpose of tourism or business. Second, virtual mobilities involve a type of redefining of what it means to be mobile: No longer does one's body have to move, but one can experience different people, places, and events at a distance and enabled by technologies such as the mobile telephone and, especially, the Internet. Such technologies are said to dematerialize space because they bypass it, making it irrelevant to social interaction and constructing through the computer screen a type of stationary wanderer who is able to be co-present with others via mediated forms that do not rely on direct bodily presence. Third is imagined and imaginative mobility, based on the desire for various types of mobile experiences associated with tourism, such as journey planning, anticipating, and daydreaming about journeys or travel. 总结——Conclusion A number of important critical issues arise whenever ideas of mobility are considered. The emphasis on an ultra porous and geographically unbounded world that affords some citizens a wide degree of corporeal and cultural mobilities is bound to invite criticism that mobility is a middle-class, Western-centric habit cultivated by the contemporary world. The experience of mobility is both globally and, as far as individual societies are concerned, structurally unequal. Mobility is associated with freedom of movement but also with its direct opposite, as the stories of refugees attest. The mobilities of things-including people-cannot be characterized as a set of perfectly fluid, open flows of movement. All mobile things find resistances, blockages, and boundaries. Furthermore, when talking about the mobility of people, one must confront questions of the relative role of agency and structure in affording mobility, and one must deal with questions of volition and the desire for mobility, based on things such as occupation, an aspiration to see beyond one's local setting, or a desire to seek new experiences. These disclaimers notwithstanding, increased mobilities in space are the marker of modern social life and constitute and important field of cutting-edge study within sociology and allied disciplines such as geography, economics, and urban planning. 结束说明——End Notes Urry, J. (2007). Mobilities. Cambridge, UK: Polity. Pp 90-99 Adey, P. (2006). If mobility is everything then it is nothing: Towards a relational politics of (im) mobilities. Mobilities vol. 1 pp. 75-94. Cresswell, T. (2006). On the move: Mobility in the modern Western world. London: Routledge. Pp 78-90 Brockmann D., L. Hufnagel3& T. Geisel1,2,4. 2006 "The scaling laws of human travel". 1Max-Planck Institute for Dynamics and Self-Organisation, Germany. 2Department of Physics, University of Go?¨ttingen, Germany. 3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California. 4Bernstein Center for Computational Neuroscience, Germany. Pp 56-78 Featherstone, M. , ed. , Thrift, N. , ed. , & Urry, J. (Eds.). (2005). Automobilities. London: Sage. Pp 90-95 Frello, B. (2008).Towards a discursive analytics of movement: On the making and unmaking of movement as an object of knowledge. Mobilities vol. 3 no. (1) pp. 25-50. Injong Rhee, Minsu Shin, Seongik Hong NC State University. Kyunghan Lee, Song Chong 2008. School of EECS, KAIST. " On the Levy-walk Nature of Human Mobility" . pp 67-89 Kyunghan Lee (KAIST), Seongik Hong (NCSU), SeongJoon Kim (NCSU), Injong Rhee (NCSU) and Song Chong (KAIST) 2009. " SLAW: A Mobility Model for Human Walks". Pp 54-78 Ming Zhao, 2008 Levi Mason, and Wenye Wang. "Empirical Study on Human Mobility for Mobile Wireless Networks". North Carolina State University, Raleigh, NC 27695. Pp 56-78 Seongik Hong, Kyunghan Lee, and Injong Rhee. 2010 "STEP: A Spatio-Temporal Mobility Model for Humans Walks". North Carolina State University, USA. Pp 90-112 Sheller, M. and Urry, J. (2006). The new mobilities paradigm. Environment and Planning A vol. 38 pp. 207-226. Tiago S. Azevedo, Rafael L. Bezerra, Carlos A. V. Campos and Lu?′?±s F. M. de Moraes. 2009 "An Analysis of Human Mobility using Real Traces". Federal University of Rio de Janeiro. Pp 67-75 Uteng, T. , ed. , & Cresswell, T. (Eds.). (2008). Gendered mobilities. Aldershot, UK: Ashgate. Pp 56-78 V. V. Belik1 , T. Geisel1,2 , and D. Brockmann 2009. "The impact of human mobility on spatial disease dynamics". 1Max-Planck-Institute for Dynamics and Self-Organization,Gttingen, Germany. 2Georg-August-University, G?ttingen, Germany. 3Northwestern University, Evanston IL, USA. Pp 56-89 Verstraete, G. , ed. , & Cresswell, T. (Eds.). (2002). Mobilizing place, placing mobility: The politics of representation in a globalized world. Amsterdam: Rodopi. Pp 23-35 Human mobility models A survey of the existing human mobility models; these are some examples: Models that describes human walk by Levy flights Statistics that is relevant to generating human mobility models. Fig. shows statistics on direction, velocity and correlation of flight lengths and directions over time series. These statistics are not explicitly specified in Levy walk models, but are useful in generating human mobility tracks for simulation. From our data, we find that while most scenarios produce close to a uniform distribution of turning angles, the New York City traces have more bias in particular directions mostly in 90 and 270 degrees. This pattern is likely related to geographical artifacts since Manhattan tends to induce more perpendicular directional changes. Fig. (a) shows the turning angle distribution from New York City traces produced based on the angle model with a?? = 30. The angle distributions show the effect of the shapes of geographical constraints. The speed of human mobility has high correlation with flight lengths: velocity increases as flight lengths increase. Constant velocity is a common assumption in Levy walks. Fig.(b) depicts the correlation between flight lengths and velocity. We also measure auto-correlation of flight lengths and turning angles over the time series of flight length and turning angle samples. We find some auto-correlation of flight lengths over up to 10 sample lags while almost no auto-correlation of turning angles (in some cases, we find some negative correlation around one or two lags).#p#分页标题#e# We did not find any significant difference of these statistics over different scenarios. Fig. (c) Shows representative auto-covariance coefficients. The significant auto-correlation of flight lengths indicate that when small flights are made, there are non-zero preference for similar sizes near future. This pattern cannot be described by random walks (including Levy walks) as they produce flights randomly without any dependency on the past history of flights. Random Models: Random Walk (RW), Brownian and Random Waypoint Walk The BM model uses ± = 2 and RWP chooses a random destination uniformly within the simulation area. The pause time distributions of these models are set the same as that in the LW model. All the simulation runs are ensured to be in their stationary regimes as all the mobility models have finite pause time and trip duration and we discard the first 100 hours of simulation results to avoid transient effects as shown in [18]. All models use the same velocity model discussed in V-A. Compared to BM's ICT distribution, the ICT distribution of Levy walks fits much better to the measured ICT distribution in UCSD. We are able to fit the power-law slope and also approximate the exponential decay at the tail portion of the measured data. Although there could be other types of mobility patterns that could generate the same ICT distributions as UCSD's, this result allows us to conjecture that the actual mobility that generates these characteristics in these settings is more closely modeled by Levy walks than BM. Furthermore, the ICT distribution patterns of various mobility models are closely related to their diffusion rates. In RWP, the mobility is the most diffusive and in BM it is the least. In LW, the diffusivity is in-between and with smaller value of ± it becomes more diffusive. The more diffusive the mobility is the shorter tail its ICT distribution becomes. To confirm this pattern, we run Levy walks with various ± while fixing ?2 to one. Fig. 10(b) shows that as ± gets smaller, the tail distribution of ICT becomes shorter. Mobility models with spatial and temporal dependency: such as Gauss-Markov Mobility Model. Mobility models with geographic restriction: such as Pathway Mobility Model Flight truncations are natural consequences of geographical constraints including boundaries and physical obstructions, and observation artifacts (e.g., we do not consider those flights that leave the area boundary). All the distributions in Fig. 5 suffer from truncations of flights longer than a few kilometers whose effects are shown as sharp drops in the frequency of very long flights. This effect shows up evidently with State fair traces shown in Fig. where even short-tail distributions fit well. The State fair traces are obtained from a highly confined area of less than 350 meter radius (it is smallest among the five sites). Thus, it is subject to more truncations. The sharp drops at the tails give rise to a possibility that the flight distributions have long-tails but not power tails since truncated power law distributions can be also fitted with non power-law long-tail distributions such as Weibull. (This truncation problem also appears in earlier studies of animal mobility,) Our data is inconclusive in disproving this. However, there are some hints that this may not be the case. Fig Shows the CCDF of flights as we increase the flight angle in the flight model. We find that as the angle increases, the distribution becomes flatter with a heavier tail. Under the pause-based model (i.e., a?? = 180), it shows the heaviest tail. While it seems obvious that the frequency of longer flights increases with more angle tolerance in the flight model, this phenomenon also reveals an important feature in human mobility patterns: if we accept that humans tend to pause for a non-zero period of time when they get to a destination, the heavier-tail distribution of flights for the pause-based model implies that it is human intention causing the heavy-tail tendency, not the geographical constraints that force humans to make short flights with no pause. This also implies the scale-free tendency of the flight distribution: as we increase the scale by removing constraints and boundaries or increasing the observation area, we are expected to see longer flights. It does not make sense that human intention to move to a destination is bounded by some invisible boundaries as in Weibull. The power-law tendency of human mobility over a larger scale [14] also provides hints for this scale-freedom and self-similarity. This human intention is not well described by pure non-power-law long-tail distributions.
Brief comparison between these models
Applications of human mobility models: Such as: While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model not only accounts for the empirically observed scaling laws but also allows us to analytically predict most of the pertinent scaling exponents. Uncovering the statistical patterns that characterize the trajectories humans follow during their daily activity is not only a major intellectual challenge, but also of importance for public health 1-5, city planning 6-8, traffic engineering 9, 10 and economic forecasting 11. For example, quantifiable models of human mobility are indispensable for predicting the spread of biological pathogens 1-5 or mobile phone viruses 12. In the past few years the availability of mobile phone records, GPS data, and other datasets capturing aspects of human mobility have given a new empirically driven momentum to the subject. While the available datasets significantly differ in their reach and resolution, the results appear to agree on a number of quantitative characteristics of human mobility. For example, both dollar bill tracking 13 and mobile phone data 14 indicate that the aggregated jump size (”r) and waiting time (?”t) distributions characterizing human trajectories are fat-tailed, i.e. 1, where ”r denotes the distances covered by an individual between consecutive sightings, and ”t is the time spent by an individual at the same location. These findings suggest that human trajectories are best described as Levy Flights (LF) or continuous time random walks (CTRW), a much studied modeling framework in the random walk (RW) community 13, 15-20.
The purpose of the present paper is to show, using a series of direct measurements, that human trajectories do follow several highly reproducible scaling laws. Yet, many of these laws are either not explained by the CTRW model, or they are in direct contradiction with the CTRW predictions, indicating the lack of modeling framework capable of capturing the basic features of human mobility. To explain the origin of the observed scaling laws, we introduce two principles that govern human mobility, serving as the starting point of a statistically acceptable microscopic model for individual human motion. We show that the model can account for the empirically observed scaling laws and allows us to analytically predict the pertinent scaling exponents.
Scaling Anomalies We used two datasets to uncover the patterns characterizing individual mobility. The first dataset (D1) captures for a one-year period the time-resolved trajectories of 3 million anonymized mobile phone users. Each time a user initiated or received a phone call the tower that routed the communication was recorded for billing purposes. Thus, the user's location was recorded with the resolution that is determined by the local tower density. The reception area of a tower varies from as little as a few hundred meters in metropolitan area to a few kilometers in rural regions, controlling our uncertainty about the user's precise location. However, since here we focus on the asymptotic scaling properties of human trajectories, these short distance uncertainties are not expected to affect our results (see Supplementary Material Section S1). The second dataset (D2) uses the anonymized location record of 1,000 users who signed up for a location based service, thus their location was recorded every hour for a two week period. As a first step we calculated the displacement at hourly intervals, finding - and an expected cutoff at ”r ~ 100 km, corresponding to the distance people could reasonably cover in an hour. We used the D2 dataset to measure P(”t), where the waiting time ”t is defined as the time a user spent at one location. We find that P(”t) follows - = 0.8±0.1 and a cutoff of ”t = 17 hours, likely capturing the typical awake period of an individual. Taken together, the fat-tailed nature of P(”r) and P(”t) suggest that human follow a CTRW during their daily mobility. Next we discuss three empirical observations that indicate that human trajectories follow reproducible scaling laws, but also illustrate the shortcoming of the CTRW model in capturing the observed scaling properties: The number of distinct locations S(t) visited by a randomly moving object is expected to follow 21-23#p#分页标题#e#
S(t) ~ t ,
where = 1 for Lévy flights 24 and = 2 for CTRW. Interestingly, our measurements indicate that for humans = 0.6±0.02 (see Fig. 1a), smaller than the CTRW prediction of ?2 = 0.8?±0.1. The fact that < 1 indicates a slow-down at large time scales, a deceasing tendency of the user to visit previously unvisited locations.
Visitation frequency: The probability f of a user to visit a given location is expected to be asymptotically (ta’a) uniform everywhere (f ~ const.) for both LF and CTRW. In contrast, the visitation patterns of humans is rather uneven, so that the frequency f of the kth most visited location follows Zipf's law 14
fk ~ k -′,
where ′ a‰ 1.2 ± 0.1 (see Fig. 1b). This suggests that the visitation frequency distribution follows P(f) ~ f -(1+1/′).
Ultra-slow diffusion: The CTRW model predicts that the mean square displacement (MSD) asymptotically follows with v = 22/± a‰ 3.1. Since both P(”r) and P(”t) have cutoffs, asymptotically the MSD should converge to a Brownian behavior with v = 1. However, this convergence is too slow25 to be relevant in our observational time frame. Either way, CTRW predicts that the longer we follow a human trajectory, the further it will drift from its initial position. Yet, humans have a tendency to return home on daily basis, suggesting that simple diffusive processes, that are not recurrent in two dimensions, do not offer a suitable description of human mobility. Indeed, our measurements indicate an ultra-slow diffusive process, in which the MSD appears to follow a slower than logarithmic growth (see Fig. 1c and Ref. 14). Such ultra-slow growth of the MSD is rare in diffusion, having been observed before only in a few disordered systems, from glasses (for example the Sinai model 26) to polymers 27 and iterated maps 28. On one end, the findings summarized in A - C indicate that individual human mobility does follow reproducible scaling laws, whose origins remain to be uncovered. Yet, they also document systematic deviations from the predictions of the LF or CTRW based null models. The main purpose of this paper is to offer a model that not only explains the origin of the anomalies A - C, but also leads to a self-consistent statistical model of individual human mobility.
Generic Mechanisms and Individual Mobility Model
As we build our model, we will take for granted the observations that the jump size P(”r) and the waiting time P(”t) distributions characterizing individual human trajectories are heavy tailed, a phenomenon addressed by a series of models 29-33. Yet, P(”r) and P(”t) alone are not sufficient to explain the scaling laws A - C. We propose that the main reason for this discrepancy is that two generic mechanisms, exploration and preferential return, unique to human mobility, are missing from the traditional random walk (LF or CTRW) models: (1) Exploration: Random walk models assume that the next diffusive step is independent of the previously visited locations. In contrast, the scaling law (1) indicates that the tendency to explore additional locations decreases with time. Indeed, the longer we observe a person's trajectory, the harder is to find locations in the vicinity of their home/workplace that they have not yet visited. (2) Preferential Return: In contrast with the RW based models for which the visitation probability is random and uniform in space, humans show significant propensity to return to the locations they visited frequently before, like home or workplace. In what follows we present an individual mobility (IM) model that incorporates ingredients (1) and (2), showing that they are sufficient to explain the anomalies A - C. The model, intended to describe the trajectory of an individual, assumes that at time t = 0 the individual is at some preferred location (see Fig. 2). After a waiting time ”t chosen from the P(”t) distribution, the individual will change its location. We assume that the individual has two choices: Exploration: With probability Pnew = S -3
the individual moves to a new location (different from the S locations it visited before). The distance ”r that it covers during this exploratory jump is chosen from the P(”r) distribution and its direction is selected to be random. As the individual moves to this new position, the number of previously visited locations increases from S to S+1.
Preferential Return: With the complementary probability Pret = 1 - S-3 the individual returns to one of the S previously visited locations. In this case, the probability i to visit location i is chosen to be proportional to the number of visits the user previously had to that location. That is, we assume that
i = fi,
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