Utterance Selection Model of Language Change

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.Comment: 21 pages, 17 figure

The GeV Excess Shining Through: Background Systematics for the Inner Galaxy Analysis

Recently, a spatially extended excess of gamma rays collected by the Fermi-LAT from the inner region of the Milky Way has been detected by different groups and with increasingly sophisticated techniques. Yet, any final conclusion about the morphology and spectral properties of such an extended diffuse emission are subject to a number of potentially critical uncertainties, related to the high density of cosmic rays, gas, magnetic fields and abundance of point sources. We will present a thorough study of the systematic uncertainties related to the modelling of diffuse background and to the propagation of cosmic rays in the inner part of our Galaxy. We will test a large set of models for the Galactic diffuse emission, generated by varying the propagation parameters within extreme conditions. By using those models in the analysis of Fermi-LAT data as Galactic foreground, we will show that the gamma-ray excess survives and we will quantify the uncertainties affecting the excess morphology and energy spectrum.Comment: 2014 Fermi Symposium proceedings - eConf C14102.1 7 pages, 4 figure

A Hadronic Scenario for the Galactic Ridge

Several observations from Fermi-LAT, up to few hundred GeV, and from H.E.S.S., up to $\sim$ 10 TeV, reported an intense $\gamma$-ray emission from the inner part of the Galactic plane. After the subtraction of point-like contributions, the remaining $\gamma$-ray spectrum can provide important hints about the cosmic-ray (CR) population in that region. In particular, the diffuse spectrum measured by both Fermi-LAT and H.E.S.S. in the Galactic Ridge is significantly harder with respect to the rest of the Galaxy. These results were recently interpreted in terms of a comprehensive CR transport model which, adopting a spatial dependent diffusion coefficient and convective velocity, reproduces Fermi-LAT results on the whole sky as well as local CR spectra. We showed as that model predicts a significantly harder neutrino diffuse emission compared to conventional scenarios: The predicted signal is able to account for a significant fraction of the astrophysical flux measured by IceCube. In this contribution, we use the same setup to calculate the expected neutrino flux from several windows in the inner Galactic plane and compare the results with IceCube observations and the sensitivities of Mediterranean neutrino telescopes. In particular, for the ANTARES experiment, we compare the model expectations with the upper limits obtained from a recent unblinded data-analysis focused on the galactic ridge region. Moreover, we also show the expectations from the galactic ridge for the future KM3NeT observatory, whose position is optimal to observe this portion of the sky.Comment: Oral contribution to the 34th International Cosmic Ray Conference, July 30 to August 6, The Hague, Netherland