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A schematic illustration of the random walk strategy as defined in Eq (16).

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posted on 06.03.2019, 18:39 by D. Loaiza-Monsalve, A. P. Riascos

In (a) we depict locations on the plane (represented by circles); the probability to go from location i to a different site is determined by two types of transition probabilities: , which is a constant, to a site j inside a circular region of radius R centered in the location i and , for a displacement to the site k outside the circle of radius R, that considers long-range transitions with a power-law decay proportional to , where dik is the distance between sites i and k. In (b) we present Monte Carlo simulations of a discrete-time random walker that visits the stations in BSS in the cities of Chicago and New York following the random strategy defined by the transition probabilities in Eq (16). The information of the values N, R and α used in each system is reported in Table 1. The total number of transitions between stations in each simulation is t = 100 and we assign a colored line to each of the displacements. The scale in the color bar represents the discrete time t at which each transition occur. The maps were drawn from base maps of satellite imagery (Source: http://server.arcgisonline.com/ArcGIS/rest/services/World_Shaded_Relief/MapServer) and the Matplotlib Basemap package (https://pypi.python.org/pypi/basemap/1.0.7).

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