Generalized naming game and Bayesian naming game as dynamical systems.

We study the ß model (ß-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the ß model, we demonstrate the existence of a nongeneric bifurcation with a bifurcation point ß_{c}=1/3. As ß passes through ß_{c}, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities p_{A} and p_{B} as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that p_{A}=p_{B}=p, where p is a constant.

A bird's-eye view of naming game dynamics: From trait competition to Bayesian inference.

The present contribution reviews a set of different versions of the basic naming game model, differing in the underlying topology or in the mechanisms regulating the interactions between agents. We include also a Bayesian naming game model recently introduced, which merges the social dynamics of the basic naming game model with the Bayesian learning framework introduced by Tenenbaum and co-workers. The latter model goes beyond the fixed nature of names and concepts of standard semiotic dynamics models and the corresponding one-shot learning process by describing dynamically how agents can generalize a concept from a few examples, according to principles of Bayesian inference.

Inconsistency between linearized Thomas-Fermi approximation and electron-ionized impurity scattering rate in the first Born approximation.

We show that by computing the electron-impurity scattering rate at the first order via Fermi's golden rule, and assuming that the localized impurity potential is of Yukawa form, one obtains a wave vector transfer distribution which is inconsistent with the finite temperature linearized Thomas-Fermi approximation for n-type semiconductors. Our previous findings show that this is not the case for the carrier nondegenerate dynamics, because the average wave vector transferred being in general negligible in this regime. Moreover, we examine the behavior of the electron-impurity differential cross-sections in the first Born approximation for relevant values of the wave vector transfer. We find that in the majority of collisions, the scattering probabilities differ at the most by 1% from the estimates computed by means of the impurity potential at random phase approximation level.

Spin Relaxation in GaAs: Importance of Electron-Electron Interactions.

We study spin relaxation in n-type bulk GaAs, due to the Dyakonov-Perel mechanism, using ensemble Monte Carlo methods. Our results confirm that spin relaxation time increases with the electronic density in the regime of moderate electronic concentrations and high temperature. We show that the electron-electron scattering in the non-degenerate regime significantly slows down spin relaxation. This result supports predictions by Glazov and Ivchenko. Most importantly, our findings highlight the importance of many-body interactions for spin dynamics: we show that only by properly taking into account electron-electron interactions within the simulations, results for the spin relaxation time-with respect to both electron density and temperature-will reach good quantitative agreement with corresponding experimental data. Our calculations contain no fitting parameters.