Generating the sequence using a preferential attachment based model . We apply a preferential attachment based model to generated topic tuple sequences with power - law distributed usage of each topic tuple [ 32,37,38 ] . In the model , an individual 's activity is randomly chosen from the two actions . One is to explore a new subject and publish a paper with a new topic tuple . The other is to return to a previously studied subject and publish a paper with a topic tuple already used . The probability to explore is defined as ρn −γ in which the term n −γ captures the decreasing trend to explore a new subject as the number of papers increases . Consequently the probability of return , i.e. to reuse an old topic tuple , is 1 − ρn −γ . If one returns , the choice of existing topic tuples is governed by preferential attachment : the probability p i to use a specific topic tuple i is proportional to the tuple i 's current usage , so p i = n i / j n j where n i is the number of times that the tuple i is used . The parameters applied are ρ = 0.4 and γ = 0.1 . Each individual 's time step is controlled by the number of papers published , following distribution P ( n ) ∼ n −1.5 with a cutoff n max = 150 . These variables make the sequence generated similar to those in real data . We generate totally 20,000 independent sequences , a comparable number to the size of real data . See Supplementary Discussion 4 for more about the preferential attachment based model . Data availability . The Physical Review dataset is available upon requested from the APS at http://journals.aps.org/datasets . The name disambiguation procedure and the associated data are described in Ref . [ 6,43 ] .