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      Emergence of encounter networks due to human mobility

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      PLoS ONE
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          Abstract

          There is a burst of work on human mobility and encounter networks. However, the connection between these two important fields just begun recently. It is clear that both are closely related: Mobility generates encounters, and these encounters might give rise to contagion phenomena or even friendship. We model a set of random walkers that visit locations in space following a strategy akin to Lévy flights. We measure the encounters in space and time and establish a link between walkers after they coincide several times. This generates a temporal network that is characterized by global quantities. We compare this dynamics with real data for two cities: New York City and Tokyo. We use data from the location-based social network Foursquare and obtain the emergent temporal encounter network, for these two cities, that we compare with our model. We found long-range (Lévy-like) distributions for traveled distances and time intervals that characterize the emergent social network due to human mobility. Studying this connection is important for several fields like epidemics, social influence, voting, contagion models, behavioral adoption and diffusion of ideas.

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          Most cited references69

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          Understanding individual human mobility patterns

          Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited thanks to the lack of tools to monitor the time resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six month period. We find that in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic length scale and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent based modeling.
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            The scaling laws of human travel

            The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3]. Human travelling, e.g. is responsible for the geographical spread of human infectious disease [4-9]. In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic [10] the knowledge of dynamical and statistical properties of human travel is thus of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a comprehensive dataset of over a million individual displacements we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as Levy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails which attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process.
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              The origin of bursts and heavy tails in human dynamics

              The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. Here we show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experience very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. These findings have important implications from resource management to service allocation in both communications and retail.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ResourcesRole: SoftwareRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ResourcesRole: SoftwareRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2017
                12 October 2017
                : 12
                : 10
                : e0184532
                Affiliations
                [1 ] Department of Civil Engineering, Universidad Mariana, San Juan de Pasto, Colombia
                [2 ] Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México, México
                East China University of Science and Technology, CHINA
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0002-9243-3246
                Article
                PONE-D-17-17253
                10.1371/journal.pone.0184532
                5638260
                29023458
                70e3ec10-5047-4d96-82db-3869a4b709ed
                © 2017 Riascos, Mateos

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 4 May 2017
                : 25 August 2017
                Page count
                Figures: 10, Tables: 1, Pages: 22
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100007045, Secretaría de Ciencia, Tecnología e Innovación del Distrito Federal;
                Award Recipient :
                A.P.R. acknowledges support from the Secretaría de Ciencia, Tecnología e Innovación (SECITI), the Centro Latinoamericano de Física (CLAF), and the Consejo Nacional de Ciencia y Tecnología (CONACYT), México: The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Mathematical Models
                Random Walk
                Research and analysis methods
                Mathematical and statistical techniques
                Statistical methods
                Monte Carlo method
                Physical sciences
                Mathematics
                Statistics (mathematics)
                Statistical methods
                Monte Carlo method
                Computer and Information Sciences
                Network Analysis
                Social Networks
                Social Sciences
                Sociology
                Social Networks
                Earth Sciences
                Geography
                Human Geography
                Human Mobility
                Social Sciences
                Human Geography
                Human Mobility
                Physical Sciences
                Mathematics
                Probability Theory
                Probability Distribution
                Physical Sciences
                Mathematics
                Algebra
                Linear Algebra
                Eigenvectors
                Physical Sciences
                Mathematics
                Geometry
                Radii
                Physical Sciences
                Mathematics
                Algebra
                Linear Algebra
                Eigenvalues
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

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                Uncategorized

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