01973nas a2200229   4500008004100000022001400041245005100055210005100106300000700157490000600164520131800170100002301488700001701511700002101528700002801549700001901577700002201596700002001618700001801638700002301656856006401679       2018                        eng d  a2296-424X00aRank Dynamics of Word Usage at Multiple Scales0 aRank Dynamics of Word Usage at Multiple Scales  a450 v63 aThe recent dramatic increase in online data availability has allowed researchers to explore human culture with unprecedented detail, such as the growth and diversification of language. In particular, it provides statistical tools to explore whether word use is similar across languages, and if so, whether these generic features appear at different scales of language structure. Here we use the Google Books $N$-grams dataset to analyze the temporal evolution of word usage in several languages. We apply measures proposed recently to study rank dynamics, such as the diversity of $N$-grams in a given rank, the probability that an $N$-gram changes rank between successive time intervals, the rank entropy, and the rank complexity. Using different methods, results show that there are generic properties for different languages at different scales, such as a core of words necessary to minimally understand a language. We also propose a null model to explore the relevance of linguistic structure across multiple scales, concluding that $N$-gram statistics cannot be reduced to word statistics. We expect our results to be useful in improving text prediction algorithms, as well as in shedding light on the large-scale features of language use, beyond linguistic and cultural differences across human populations.1 aMorales, José, A.1 aColman, Ewan1 aSánchez, Sergio1 aSánchez-Puig, Fernanda1 aPineda, Carlos1 aIñiguez, Gerardo1 aCocho, Germinal1 aFlores, Jorge1 aGershenson, Carlos  uhttps://www.frontiersin.org/article/10.3389/fphy.2018.0004502428nas a2200229   4500008004100000022001400041245007400055210006900129300000700198490000600205520173500211100002301946700002101969700001801990700001902008700002302027700002002050700002302070700002902093700002202122856005402144       2016                        eng d  a2193-112700aGeneric temporal features of performance rankings in sports and games0 aGeneric temporal features of performance rankings in sports and   a330 v53 aMany complex phenomena, from trait selection in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the worldwide wealth distribution. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are generic mechanisms of stratification common to many systems. Human sports and games, with their (varied but simple) rules of competition and measures of performance, serve as an ideal test-bed to look for universal features of hierarchy formation. With this goal in mind, we analyse here the behaviour of performance rankings over time of players and teams for several sports and games, and find statistical regularities in the dynamics of ranks. Specifically the rank diversity, a measure of the number of elements occupying a given rank over a length of time, has the same functional form in sports and games as in languages, another system where competition is determined by the use or disuse of grammatical structures. We use a Gaussian random walk model to reproduce the rank diversity of the studied sports and games. We also discuss the relation between rank diversity and the cumulative rank distribution. Our results support the notion that hierarchical phenomena may be driven by the same underlying mechanisms of rank formation, regardless of the nature of their components. Moreover, such regularities can in principle be used to predict lifetimes of rank occupancy, thus increasing our ability to forecast stratification in the presence of competition.1 aMorales, José, A.1 aSánchez, Sergio1 aFlores, Jorge1 aPineda, Carlos1 aGershenson, Carlos1 aCocho, Germinal1 aZizumbo, Jerónimo1 aRodríguez, Rosalío, F.1 aIñiguez, Gerardo  uhttp://dx.doi.org/10.1140/epjds/s13688-016-0096-y