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We analyze the time evolution of a system of two coexisting languages (Castillian Spanish and Galician, both spoken in northwest Spain) in the framework of a model given by Abrams and Strogatz [Nature 424, 900 (2003)]. It is shown that, contrary to the models initial prediction, a stable bilingual situation is possible if the languages in competition are similar enough. Similarity is described with a simple parameter, whose value can be estimated from fits of the data.
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Human languages evolve continuously, and a puzzling problem is how to reconcile the apparent robustness of most of the deep linguistic structures we use with the evidence that they undergo possibly slow, yet ceaseless, changes. Is the state in which we observe languages today closer to what would be a dynamical attractor with statistically stationary properties or rather closer to a non-steady state slowly evolving in time? Here we address this question in the framework of the emergence of shared linguistic categories in a population of individuals interacting through language games. The observed emerging asymptotic categorization, which has been previously tested - with success - against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system. This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems. We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.
In this paper, a baseline model termed as random birth-and-death network model (RBDN) is considered, in which at each time step, a new node is added into the network with probability p (0<p <1) connect it with m old nodes uniformly, or an existing node is deleted from the network with probability q=1-p. This model allows for fluctuations in size, which may reach many different disciplines in physics, ecology and economics. The purpose of this study is to develop the RBDN model and explore its basic statistical properties. For different p, we first discuss the network size of RBDN. And then combining the stochastic process rules (SPR) based Markov chain method and the probability generating function method, we provide the exact solutions of the degree distributions. Finally, the characteristics of the tail of the degree distributions are explored after simulation verification. Our results show that the tail of the degree distribution for RBDN exhibits a Poisson tail in the case of 0<p<=1/2 and an exponential tail as p approaches to 1.
The primordial confrontation underlying the existence of our universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution (or rather involution) going uniformly and monotonically from birth to death. Since the 19th century, this concept is one of the cornerstones and in the same time puzzles of statistical mechanics. On the other hand, there is the empirical experience where one witnesses the emergence, growth and diversification of new self-organized objects with ever-increasing complexity. When modeling them in terms of simple discrete elements one finds that the emergence of collective complex adaptive objects is a rather generic phenomenon governed by a new type of laws. These emergence laws, not connected directly with the fundamental laws of the physical reality, nor acting in addition to them but acting through them were called by Phil Anderson More is Different, das Maass by Hegel etc. Even though the emergence laws act through the intermediary of the fundamental laws that govern the individual elementary agents, it turns out that different systems apparently governed by very different fundamental laws: gravity, chemistry, biology, economics, social psychology, end up often with similar emergence laws and outcomes. In particular the emergence of adaptive collective objects endows the system with a granular structure which in turn causes specific macroscopic cycles of intermittent fluctuations.
Publication statistics are ubiquitous in the ratings of scientific achievement, with citation counts and paper tallies factoring into an individuals consideration for postdoctoral positions, junior faculty, tenure, and even visa status for international scientists. Citation statistics are designed to quantify individual career achievement, both at the level of a single publication, and over an individuals entire career. While some academic careers are defined by a few significant papers (possibly out of many), other academic careers are defined by the cumulative contribution made by the authors publications to the body of science. Several metrics have been formulated to quantify an individuals publication career, yet none of these metrics account for the dependence of citation counts and journal size on time. In this paper, we normalize publication metrics across both time and discipline in order to achieve a universal framework for analyzing and comparing scientific achievement. We study the publication careers of individual authors over the 50-year period 1958-2008 within six high-impact journals: CELL, the New England Journal of Medicine (NEJM), Nature, the Proceedings of the National Academy of Science (PNAS), Physical Review Letters (PRL), and Science. In comparing the achievement of authors within each journal, we uncover quantifiable statistical regularity in the probability density function (pdf) of scientific achievement across both time and discipline. The universal distribution of career success within these arenas for publication raises the possibility that a fundamental driving force underlying scientific achievement is the competitive nature of scientific advancement.
We review the task of aligning simple models for language dynamics with relevant empirical data, motivated by the fact that this is rarely attempted in practice despite an abundance of abstract models. We propose that one way to meet this challenge is through the careful construction of null models. We argue in particular that rejection of a null model must have important consequences for theories about language dynamics if modelling is truly to be worthwhile. Our main claim is that the stochastic process of neutral evolution (also known as genetic drift or random copying) is a viable null model for language dynamics. We survey empirical evidence in favour and against neutral evolution as a mechanism behind historical language changes, highlighting the theoretical implications in each case.
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