No Arabic abstract
A spectacular order-order-like transition is presented in the distribution of hagiotoponyms in France. Data analysis and displays distinguish male and female cases. The respective hapax values point to a very large variety of saints with a specific devotion. The most popular ones are St. Martin and the apostles. The less popular ones are not so well known. These features are explained in terms of herding in agent behaviors: people have either preferred popular saints with supposedly good links to God, whence a herding behavior, or (non-herding) agents have preferred to name their local human settlement through a reference to some holy person(s) with more local specificities -- yet with moral or religious leadership, and conjectured to have good contact with God, whence at least locally defined as a saint.
Here we study the emergence of spontaneous leadership in large populations. In standard models of opinion dynamics, herding behavior is only obeyed at the local scale due to the interaction of single agents with their neighbors; while at the global scale, such models are governed by purely diffusive processes. Surprisingly, in this paper we show that the combination of a strong separation of time scales within the population and a hierarchical organization of the influences of some agents on the others induces a phase transition between a purely diffusive phase, as in the standard case, and a herding phase where a fraction of the agents self-organize and lead the global opinion of the whole population.
Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent $alpha<2$, unlike preferential-attachment models), similar to those seen in empirical data.
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks, or duplication. Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity. We develop a framework where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.
In social tagging systems, the diversity of tag vocabulary and the popularity of such tags continue to increase as they are exposed to selection pressure derived from our cognitive nature and cultural preferences. This is analogous to living ecosystems, where mutation and selection play a dominant role. Such population dynamism, which yields a scaling law, is mathematically modeled by a simple stochastic process---the Yule--Simon process, which describes how new words are introduced to the system and then grow. However, in actual web services, we have observed that a large fluctuation emerges in the popularity growth of individual tags that cannot be explained by the ordinary selection mechanism. We introduce a scaling factor to quantify the degree of the deviation in the popularity growth from the mean-field solution of the Yule--Simon process, and we discuss possible triggers of such anomalous popularity behavior.
The digital age allows data collection to be done on a large scale and at low cost. This is the case of genealogy trees, which flourish on numerous digital platforms thanks to the collaboration of a mass of individuals wishing to trace their origins and share them with other users. The family trees constituted in this way contain information on the links between individuals and their ancestors, which can be used in historical demography, and more particularly to study migration phenomena. This article proposes to use the family trees of 238, 009 users of the Geneanet website, or 2.5 million (unique) individuals, to study internal migration. The case of 19th century France is taken as an example. Using the geographical coordinates of the birthplaces of individuals born in France between 1800 and 1804 and those of their descendants, we study migration between generations at several geographical scales. We start with a broad scale, that of the departments, to reach a much finer one, that of the cities. Our results are consistent with those of the literature traditionally based on parish or civil status registers. The results show that the use of collaborative genealogy data not only makes it possible to recover known facts in the literature, but also to enrich them.