Figure 4
Proposed model of human-interest dynamics and predicted scaling relations.
(a) Schematic illustration of the model, where an individual can enter one of the two dynamically complementary states at each hopping step: exploring new interests with the probability ρn−λ (the state of “Exploration”, the white circles representing available new interests) or returning preferentially to a previously explored interest with the probability 1 − ρn−λ (the state of “Preferential return”, the circles of different colors illustrating those visited interests, with the size corresponding to their frequencies to be visited by users). Regardless of which state takes place, as one interest is selected, an inertial effect was triggered, which can be modeled as an excited random walk (ERW)54. (b, c) Fat-tailed distribution of P(l) and P(τ), respectively. (d, e) Predicted interest-ranking distribution and transition-probability pattern, respectively. These results are obtained from model simulations where the number of agents in each case is 1000, for the parameter setting of λ = 0.4 and ρ = 0.6. For P(l), analytic result can be derived: P(l) ~ l−(2−ζ), where ζ and 1 − ζ are the probabilities of moving towards the “right” or the “left”, respectively. In (b–d), three values of ζ are used: ζ = 0.4, ζ = 0.5 and ζ = 0.6. In (e), the value of ζ is 0.5.
