In-depth analysis of the Naming Game dynamics: the homogeneous mixing case

Language emergence and evolution has recently gained growing attention through multi-agent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding.Comment: 30 pages, 19 figures (few in reduced definition). In press in IJMP

Long Time Results for a Weakly Interacting Particle System in Discrete Time

We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in $\mathbb{R}^d$, described in terms of a general stochastic evolution equation. In a setting where the state space of the particles is compact such questions have been studied in previous works, however for the case of an unbounded state space very few results are available. Under suitable assumptions on the problem data we study several time asymptotic properties of the $N$-particle system and the associated nonlinear Markov chain. In particular we show that the evolution equation for the law of the nonlinear Markov chain has a unique fixed point and starting from an arbitrary initial condition convergence to the fixed point occurs at an exponential rate. The empirical measure $\mu_{n}^{N}$ of the $N$-particles at time $n$ is shown to converge to the law $\mu_{n}$ of the nonlinear Markov process at time $n$, in the Wasserstein-1 distance, in $L^{1}$, as $N\to \infty$, uniformly in $n$. Several consequences of this uniform convergence are studied, including the interchangeability of the limits $n\to \infty$ and $N\to\infty$ and the propagation of chaos property at $n = \infty$. Rate of convergence of $\mu_{n}^{N}$ to $\mu_{n}$ is studied by establishing uniform in time polynomial and exponential probability concentration estimates

Energy-scales convergence for optimal and robust quantum transport in photosynthetic complexes

Underlying physical principles for the high efficiency of excitation energy transfer in light-harvesting complexes are not fully understood. Notably, the degree of robustness of these systems for transporting energy is not known considering their realistic interactions with vibrational and radiative environments within the surrounding solvent and scaffold proteins. In this work, we employ an efficient technique to estimate energy transfer efficiency of such complex excitonic systems. We observe that the dynamics of the Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport due to a convergence of energy scales among all important internal and external parameters. In particular, we show that the FMO energy transfer efficiency is optimum and stable with respect to the relevant parameters of environmental interactions and Frenkel-exciton Hamiltonian including reorganization energy $\lambda$, bath frequency cutoff $\gamma$, temperature $T$, bath spatial correlations, initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. We identify the ratio of \lambda T/\gamma\*g as a single key parameter governing quantum transport efficiency, where g is the average excitonic energy gap.Comment: minor revisions, removing some figures, 19 pages, 19 figure

Conformally invariant scaling limits in planar critical percolation

This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site percolation on the triangular lattice. We also give an introductory account of Schramm-Loewner evolutions (SLE(k)), a one-parameter family of conformally invariant random curves discovered by Schramm (2000). The article is organized around the aim of proving the result, due to Smirnov (2001) and to Camia and Newman (2007), that the percolation exploration path converges in the scaling limit to chordal SLE(6). No prior knowledge is assumed beyond some general complex analysis and probability theory.Comment: 55 pages, 10 figure

Parallel simulation of Population Dynamics P systems: updates and roadmap

Population Dynamics P systems are a type of multienvironment P systems that serve as a formal modeling framework for real ecosystems. The accurate simulation of these probabilisticmodels, e.g. with Direct distribution based on Consistent Blocks Algorithm, entails large run times. Hence, parallel platforms such as GPUs have been employed to speedup the simulation. In 2012, the first GPU simulator of PDP systems was presented. However, it was able to run only randomly generated PDP systems. In this paper, we present current updates made on this simulator, involving an input modu le for binary files and an output module for CSV files. Finally, the simulator has been experimentally validated with a real ecosystem model, and its performance has been tested with two high-end GPUs: Tesla C1060 and K40.Ministerio de Economía y Competitividad TIN2012-37434Junta de Andalucía P08-TIC-0420

Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed \emph{coding theorem method} the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal format, R package at http://cran.r-project.org/web/packages/acss/index.htm

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Sorting, Peers and Achievement of Aboriginal Students in British Columbia

We use administrative data on students in grades 4 and 7 in British Columbia to examine the extent to which differences in school environment contribute to the achievement gap between Aboriginal and non-Aboriginal students as measured by standardized test scores. We find that segregation of Aboriginal and non-Aboriginal students is substantial, and that differences in the distribution of these two groups across schools account for roughly half the overall achievement gap on the Foundation Skills Assessment tests in grade 7. The substantial school-level segregation of Aboriginal and non-Aboriginal student across schools means that Aboriginal students on average have a higher proportion of peers who are themselves Aboriginal, as well as a higher proportion of peers in special education. We estimate the effect of peer composition on value-added exam outcomes, using longitudinal data on multiple cohorts of students together with school-by-grade fixed effects to account for endogenous selection into schools. We find that having a greater proportion of Aboriginal peers, if anything, improves the achievement of Aboriginal students.Aboriginal education, peer effects