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  • 1.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Baek, Seung Ki
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    A Paradoxical Property of the Monkey Book2011In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P07013-Article in journal (Refereed)
    Abstract [en]

    A 'monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a 'spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a 'monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.

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  • 2.
    Rocha, Luis E C
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Structural evolution of the Brazilian airport network2009In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. 04020-Article in journal (Refereed)
    Abstract [en]

    The aviation sector is profitable, but sensitive to economic fluctuations, geopolitical constraints and governmental regulations. As for other means of transportation, the relation between origin and destination results in a complex map of routes, which can be complemented with information associated with the routes themselves, for instance, frequency, traffic load and distance. The theory of networks provides a natural framework for investigating the dynamics on the resulting structure. Here, we investigate the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo. Some structural features are in accordance with previous results for other airport networks. The analysis of the evolution of the BAN shows that its structure is dynamic, with changes in the relative relevance of some airports and routes. The results indicate that the connections converge to specific routes. The network shrinks at the route level but grows in number of passengers and amount of cargo, which more than doubled during the period studied.

  • 3.
    Vranić, Ana
    et al.
    Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Smiljanic, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics. Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Dankulov, Marija Mitrović
    Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Universal growth of social groups: empirical analysis and modeling2022In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2022, no 12, article id 123402Article in journal (Refereed)
    Abstract [en]

    Social groups are fundamental elements of any social system. Their emergence and evolution are closely related to the structure and dynamics of a social system. Research on social groups was primarily focused on the growth and the structure of the interaction networks of social system members and how members’ group affiliation influences the evolution of these networks. The distribution of groups’ size and how members join groups has not been investigated in detail. Here we combine statistical physics and complex network theory tools to analyze the distribution of group sizes in three data sets, Meetup groups based in London and New York and Reddit. We show that all three distributions exhibit log-normal behavior that indicates universal growth patterns in these systems. We propose a theoretical model that combines social and random diffusion of members between groups to simulate the roles of social interactions and members’ interest in the growth of social groups. The simulation results show that our model reproduces growth patterns observed in empirical data. Moreover, our analysis shows that social interactions are more critical for the diffusion of members in online groups, such as Reddit, than in offline groups, such as Meetup. This work shows that social groups follow universal growth mechanisms that need to be considered in modeling the evolution of social systems.

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