Inferring the Origin Locations of Tweets with Quantitative Confidence

Social Internet content plays an increasingly critical role in many domains, including public health, disaster management, and politics. However, its utility is limited by missing geographic information; for example, fewer than 1.6% of Twitter messages (tweets) contain a geotag. We propose a scalable, content-based approach to estimate the location of tweets using a novel yet simple variant of gaussian mixture models. Further, because real-world applications depend on quantified uncertainty for such estimates, we propose novel metrics of accuracy, precision, and calibration, and we evaluate our approach accordingly. Experiments on 13 million global, comprehensively multi-lingual tweets show that our approach yields reliable, well-calibrated results competitive with previous computationally intensive methods. We also show that a relatively small number of training data are required for good estimates (roughly 30,000 tweets) and models are quite time-invariant (effective on tweets many weeks newer than the training set). Finally, we show that toponyms and languages with small geographic footprint provide the most useful location signals.Comment: 14 pages, 6 figures. Version 2: Move mathematics to appendix, 2 new references, various other presentation improvements. Version 3: Various presentation improvements, accepted at ACM CSCW 201

The Flavour Portal to Dark Matter

We present a class of models in which dark matter (DM) is a fermionic singlet under the Standard Model (SM) gauge group but is charged under a symmetry of flavour that acts as well on the SM fermions. Interactions between DM and SM particles are mediated by the scalar fields that spontaneously break the flavour symmetry, the so-called flavons. In the case of gauged flavour symmetries, the interactions are also mediated by the flavour gauge bosons. We first discuss the construction and the generic features of this class of models. Then a concrete example with an abelian flavour symmetry is considered. We compute the complementary constraints from the relic abundance, direct detection experiments and flavour observables, showing that wide portions of the parameter space are still viable. Other possibilities like non-abelian flavour symmetries can be analysed within the same framework.Comment: 7 pages, 2 figures, more detailed presentation of flavour constraints, version accepted for publication in PR

First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-form

We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant algebroid structures by closed 4-forms H. The presentation is kept pedagogical and accessible to physicists as well as to mathematicians, explaining in detail in particular the interplay of field transformations in a sigma model with the type of geometrical structures induced on a target. In fact, as we also show, even if one does not know the mathematical concept of a Courant algebroid, the study of a rather general class of 3-dimensional sigma models leads one to that notion by itself. Courant algebroids became of relevance for mathematical physics lately from several perspectives - like for example by means of using generalized complex structures in String Theory. One may expect that their twisting by the curvature H of some 3-form Ramond-Ramond gauge field will become of relevance as well.Comment: 25 pages, invited contribution to the Wolfgang Kummer memorial volum

Instability of Turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (Turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.Comment: This is a new version of the paper. Presentation of results was essentially revised according to referee suggestion

Naturalness in emergent spacetime

Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are however technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small -- this is the essence of the "naturalness" problem. Herein we present an "emergent" space-time model, based on the "analogue gravity'' programme, by investigating a specific condensed-matter system that is in principle capable of simulating the salient features of an EFT framework with Lorentz violations. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore our model explicitly avoids the "naturalness problem", and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.Comment: V1:4 pages, revtex4; V2: slight changes in title, presentation, and conclusions. This version to appear in Physical Review Letter