Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts for the presence of citation bursts as well.
Wikipedia is a huge global repository of human knowledge that can be leveraged to investigate interwinements between cultures. With this aim, we apply methods of Markov chains and Google matrix for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank and CheiRank algorithms. Using automatic extraction of people names, we obtain the top 100 historical figures, for each edition and for each algorithm. We investigate their spatial, temporal, and gender distributions in dependence of their cultural origins. Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own cultures, but also the existence of global historical figures appearing in a large number of editions. By determining the birth time and place of these persons, we perform an analysis of the evolution of such figures through 35 centuries of human history for each language, thus recovering interactions and entanglement of cultures over time. We also obtain the distributions of historical figures over world countries, highlighting geographical aspects of cross-cultural links. Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to this network.
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