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Understanding mobility in a social petri dish.

Szell M, Sinatra R, Petri G, Thurner S, Latora V - Sci Rep (2012)

Bottom Line: We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas.These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics.Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

View Article: PubMed Central - PubMed

Affiliation: Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.

ABSTRACT
Despite the recent availability of large data sets on human movements, a full understanding of the rules governing motion within social systems is still missing, due to incomplete information on the socio-economic factors and to often limited spatio-temporal resolutions. Here we study an entire society of individuals, the players of an online-game, with complete information on their movements in a network-shaped universe and on their social and economic interactions. Such a "socio-economic laboratory" allows to unveil the intricate interplay of spatial constraints, social and economic factors, and patterns of mobility. We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas. These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics. Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

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Diffusion scaling in empirical data and simulated models.(a) The mean square displacement (MSD) of the positions of players follows a power relation σ2(t) ∼ tυ with a subdiffusive exponent υ ≈ 0.26. The inset shows the average probability  for a player to return after τ jumps to a sector previously visited. The curve follows a power law  with an exponent of α ≈ 1.3 and an exponential cutoff. We report, for comparison, (b) the MSD for various models of mobility. For random walkers and in the case of a Markov model with transition probability πij = mij/Σjmij we observe an initial diffusion with an exponent υ ≈ 1 and then a rapid saturation of σ2(t), due to the finite size of the network. A preferential return model also shows saturation and does not fit the empirical observed scaling exponent υ. Conversely, a model with long-time memory (Time Order Memory) reproduces the exponent almost perfectly. Such a model makes use of the empirically observed  while the Markov model and the preferential return model over-emphasize preferences to locations visited long ago and do not recreate the empirical curve well. Curves are shifted vertically for visual clarity.
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f5: Diffusion scaling in empirical data and simulated models.(a) The mean square displacement (MSD) of the positions of players follows a power relation σ2(t) ∼ tυ with a subdiffusive exponent υ ≈ 0.26. The inset shows the average probability for a player to return after τ jumps to a sector previously visited. The curve follows a power law with an exponent of α ≈ 1.3 and an exponential cutoff. We report, for comparison, (b) the MSD for various models of mobility. For random walkers and in the case of a Markov model with transition probability πij = mij/Σjmij we observe an initial diffusion with an exponent υ ≈ 1 and then a rapid saturation of σ2(t), due to the finite size of the network. A preferential return model also shows saturation and does not fit the empirical observed scaling exponent υ. Conversely, a model with long-time memory (Time Order Memory) reproduces the exponent almost perfectly. Such a model makes use of the empirically observed while the Markov model and the preferential return model over-emphasize preferences to locations visited long ago and do not recreate the empirical curve well. Curves are shifted vertically for visual clarity.

Mentions: In order to characterize the diffusion of players over the network, we have computed the mean square displacement (MSD) of their positions, σ2(t), as a function of time. Results reported in Fig. 5 (a) indicate that, for long times, the MSD increases as a power-law: with an exponent υ ≈ 0.26. This anomalous subdiffusive behaviour is not a simple effect of the topology of the Pardus universe. In fact, as shown in Fig. 5 (b), gray stars, the simulation of plain random walks on the same network produces a standard diffusion with an exponent υ ≈ 1 up to t ≈ 100 days, and then a rapid saturation effect which is not present in the case of the human players.


Understanding mobility in a social petri dish.

Szell M, Sinatra R, Petri G, Thurner S, Latora V - Sci Rep (2012)

Diffusion scaling in empirical data and simulated models.(a) The mean square displacement (MSD) of the positions of players follows a power relation σ2(t) ∼ tυ with a subdiffusive exponent υ ≈ 0.26. The inset shows the average probability  for a player to return after τ jumps to a sector previously visited. The curve follows a power law  with an exponent of α ≈ 1.3 and an exponential cutoff. We report, for comparison, (b) the MSD for various models of mobility. For random walkers and in the case of a Markov model with transition probability πij = mij/Σjmij we observe an initial diffusion with an exponent υ ≈ 1 and then a rapid saturation of σ2(t), due to the finite size of the network. A preferential return model also shows saturation and does not fit the empirical observed scaling exponent υ. Conversely, a model with long-time memory (Time Order Memory) reproduces the exponent almost perfectly. Such a model makes use of the empirically observed  while the Markov model and the preferential return model over-emphasize preferences to locations visited long ago and do not recreate the empirical curve well. Curves are shifted vertically for visual clarity.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3375635&req=5

f5: Diffusion scaling in empirical data and simulated models.(a) The mean square displacement (MSD) of the positions of players follows a power relation σ2(t) ∼ tυ with a subdiffusive exponent υ ≈ 0.26. The inset shows the average probability for a player to return after τ jumps to a sector previously visited. The curve follows a power law with an exponent of α ≈ 1.3 and an exponential cutoff. We report, for comparison, (b) the MSD for various models of mobility. For random walkers and in the case of a Markov model with transition probability πij = mij/Σjmij we observe an initial diffusion with an exponent υ ≈ 1 and then a rapid saturation of σ2(t), due to the finite size of the network. A preferential return model also shows saturation and does not fit the empirical observed scaling exponent υ. Conversely, a model with long-time memory (Time Order Memory) reproduces the exponent almost perfectly. Such a model makes use of the empirically observed while the Markov model and the preferential return model over-emphasize preferences to locations visited long ago and do not recreate the empirical curve well. Curves are shifted vertically for visual clarity.
Mentions: In order to characterize the diffusion of players over the network, we have computed the mean square displacement (MSD) of their positions, σ2(t), as a function of time. Results reported in Fig. 5 (a) indicate that, for long times, the MSD increases as a power-law: with an exponent υ ≈ 0.26. This anomalous subdiffusive behaviour is not a simple effect of the topology of the Pardus universe. In fact, as shown in Fig. 5 (b), gray stars, the simulation of plain random walks on the same network produces a standard diffusion with an exponent υ ≈ 1 up to t ≈ 100 days, and then a rapid saturation effect which is not present in the case of the human players.

Bottom Line: We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas.These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics.Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

View Article: PubMed Central - PubMed

Affiliation: Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.

ABSTRACT
Despite the recent availability of large data sets on human movements, a full understanding of the rules governing motion within social systems is still missing, due to incomplete information on the socio-economic factors and to often limited spatio-temporal resolutions. Here we study an entire society of individuals, the players of an online-game, with complete information on their movements in a network-shaped universe and on their social and economic interactions. Such a "socio-economic laboratory" allows to unveil the intricate interplay of spatial constraints, social and economic factors, and patterns of mobility. We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas. These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics. Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

Show MeSH