Phase transition in a sexual age-structured model of learning foreign languages

The understanding of language competition helps us to predict extinction and survival of languages spoken by minorities. A simple agent-based model of a sexual population, based on the Penna model, is built in order to find out under which circumstances one language dominates other ones. This model considers that only young people learn foreign languages. The simulations show a first order phase transition where the ratio between the number of speakers of different languages is the order parameter and the mutation rate is the control one.Comment: preliminary version, to be submitted to Int. J. Mod. Phys.

Simulation for competition of languages with an ageing sexual population

Recently, individual-based models originally used for biological purposes revealed interesting insights into processes of the competition of languages. Within this new field of population dynamics a model considering sexual populations with ageing is presented. The agents are situated on a lattice and each one speaks one of two languages or both. The stability and quantitative structure of an interface between two regions, initially speaking different languages, is studied. We find that individuals speaking both languages do not prefer any of these regions and have a different age structure than individuals speaking only one language.Comment: submitted to International Journal of Modern Physics

Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.Comment: 19 pages, no figure

GATA transcription factors drive initial Xist upregulation after fertilization through direct activation of a distal enhancer element

To ensure dosage compensation for X-linked genes between the sexes, one X chromosome is silenced during early embryonic development of female mammals. This process of X-chromosome inactivation (XCI) is initiated through upregulation of the RNA Xist from one X chromosome shortly after fertilization. Xist then mediates chromosome-wide gene silencing in cis and remains expressed in all cell types except the germ line and the pluripotent state, where XCI is reversed. The factors that drive Xist upregulation and thereby initiate XCI remain however unknown. We identify GATA transcription factors as potent Xist activators and demonstrate that they are essential for the activation of Xist in mice following fertilization. Through a pooled CRISPR activation screen we find that GATA1 can drive ectopic Xist expression in murine embryonic stem cells (mESCs). We demonstrate that all GATA factors can activate Xist directly via a GATA-responsive regulatory element (RE79) positioned 100 kb upstream of the Xist promoter. Additionally, GATA factors are essential for the induction of XCI in mouse preimplantation embryos, as simultaneous deletion of three members of the GATA family (GATA1/4/6) in mouse zygotes effectively prevents Xist upregulation. Thus, initiation of XCI and possibly its maintenance in distinct lineages of the preimplantation embryo is ensured by the combined activity of different GATA family members, and the absence of GATA factors in the pluripotent state likely contributes to X reactivation. We thus describe a form of regulation in which the combined action of numerous tissue-specific factors can achieve near-ubiquitous expression of a target gene

Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one, showing how spatial patterns can emerge for some values of the interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure

Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.Comment: 13 pages,6 figure

Collision dynamics of two barchan dunes simulated by a simple model

The collision processes of two crescentic dunes called barchans are systematically studied using a simple computer simulation model. The simulated processes, coalescence, ejection and reorganization, qualitatively correspond to those observed in a water tank experiment. Moreover we found the realized types of collision depend both on the mass ratio and on the lateral distance between barchans under initial conditions. A simple set of differential equations to describe the collision of one-dimensional (1D) dunes is introduced.Comment: 4 pages, 5 figures : To be published in Journal of the Physical Society of Japa

Competition and fragmentation: a simple model generating lognormal-like distributions

The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative fit that indicates the existence of a power law tail. A simple Monte Carlo model is constructed based on the processes of competition and fragmentation. The results reproduce the power law tails of the real distribution well and give better results for a poorly connected topology of interactions.Comment: 14 pages, 11 figure