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.2018.0004500950nas a2200181   4500008004100000245005900041210005900100300001200159490000900171520042400180100002100604700002000625700001800645700002300663700002200686700001900708856004100727       2018                        eng d00aTrajectory Stability in the Traveling Salesman Problem0 aTrajectory Stability in the Traveling Salesman Problem  a28260820 v20183 aTwo generalizations of the traveling salesman problem in which sites change their position in time are presented. The way the rank of different trajectory lengths changes in time is studied using the rank diversity. We analyze the statistical properties of rank distributions and rank dynamics and give evidence that the shortest and longest trajectories are more predictable and robust to change, that is, more stable.1 aSánchez, Sergio1 aCocho, Germinal1 aFlores, Jorge1 aGershenson, Carlos1 aIñiguez, Gerardo1 aPineda, Carlos  uhttps://doi.org/10.1155/2018/282608202428nas 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-y01729nas a2200181   4500008004100000245007900041210006900120260003400189300001300223490000700236520115000243100002001393700001801413700002301431700001901454700002101473856005301494       2015                        eng d00aRank Diversity of Languages: Generic Behavior in Computational Linguistics0 aRank Diversity of Languages Generic Behavior in Computational Li  bPublic Library of Sciencec04  ae01218980 v103 a<p>Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: “heads” consist of words which almost do not change their rank in time, “bodies” are words of general use, while “tails” are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.</p>
1 aCocho, Germinal1 aFlores, Jorge1 aGershenson, Carlos1 aPineda, Carlos1 aSánchez, Sergio  uhttp://dx.doi.org/10.1371%2Fjournal.pone.0121898