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The aggregated population GP is a sum of populations in all populated locations on a certain time point.
Given the distribution of population, the growth function of populated locations and the largest population size, we insert the above expressions of P s,t), l(t), and n(t) as shown in Eq. 4, Eq. 5 and Eq. 6 into Eq. 3. Then we have GP ( t ) = ∫ 1 a ∗ t b + c ( ( φ ∗ s - λ ) ∗ ( η ∗ t ε ) ∗ s ) ds = ηφ t ε 2 - λ [ ( a ∗ t b + c ) 2 - λ - 1 ].
Instead of numerating all population sizes, we use the proportion of the number of locations with population size s over the total number of populated locations, known as population distribution, which is denoted as P s, the total number of populated locations L and the largest population size N to construct the formulation of aggregated population: GP = ∑ s = 1 N P s ∗ L ∗ s, (2).
The growth of populated locations and the largest population are both power functions of time.
To specify this model, we need to study three time-dependent functions: the dynamics of population distribution P s,t), the growth function of populated locations l(t) and the growth function of the largest population n(t) in the following subsections.
To model the population growth in OSNs, one important aspect is to understand the growth of populated locations.
Similar(38)
In the temporal scale, the population growth in the largest populated location is revealed to fit a power function increasing with time.
Similar to the analysis of populated location growth, the growth of the largest population size can also be fitted using a power function as the following: n ( t ) = a ∗ t b + c. (6) Figure 3 The population growth of the largest populated location.
(a) Renren, the growth of population as a function of time in the largest populated location, follows a power function: n(t) = 155.8t1.31-1706.
(c) Gowalla, the growth of population as a function of time in the largest populated location, follows a power function: n(t) = 68.83t1.61-243.9.
(b) Twitter, the growth of population as a function of time in the largest populated location, follows a power function: n(t) = 0.19t2.97-678.8.
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