Evaluating the role of quantitative modeling in language evolution

Models are a flourishing and indispensable area of research in language evolution. Here we highlight critical issues in using and interpreting models, and suggest viable approaches. First, contrasting models can explain the same data and similar modelling techniques can lead to diverging conclusions. This should act as a reminder to use the extreme malleability of modelling parsimoniously when interpreting results. Second, quantitative techniques similar to those used in modelling language evolution have proven themselves inadequate in other disciplines. Cross-disciplinary fertilization is crucial to avoid mistakes which have previously occurred in other areas. Finally, experimental validation is necessary both to sharpen models' hypotheses, and to support their conclusions. Our belief is that models should be interpreted as quantitative demonstrations of logical possibilities, rather than as direct sources of evidence. Only an integration of theoretical principles, quantitative proofs and empirical validation can allow research in the evolution of language to progress

Updated constraints on spatial variations of the fine-structure constant

Recent work by Webb {\it et al.} has provided indications of spatial variations of the fine-structure constant, $\alpha$, at a level of a few parts per million. Using a dataset of 293 archival measurements, they further show that a dipole provides a statistically good fit to the data, a result subsequently confirmed by other authors. Here we show that a more recent dataset of dedicated measurements further constrains these variations: although there are only 10 such measurements, their uncertainties are considerably smaller. We find that a dipolar variation is still a good fit to the combined dataset, but the amplitude of such a dipole must be somewhat smaller: $8.1\pm1.7$ ppm for the full dataset, versus $9.4\pm2.2$ ppm for the Webb {\it et al.} data alone, both at the $68.3\%$ confidence level. Constraints on the direction on the sky of such a dipole are also significantly improved. On the other hand the data can't yet discriminate between a pure spatial dipole and one with an additional redshift dependence.Comment: 10 pages, 4 figure

Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation

Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its fundamentally nonlinear nature. Advances in convex relaxation theory have allowed the advent of Shor's semidefinite programming (SDP) relaxations of quadratic models of the problem. This paper shows how a recently published SDP relaxation is only exact if a very strict condition regarding turbine efficiency is observed, failing otherwise. It further proposes the use of a set of convex envelopes as a strategy to successfully obtain a stricter lower bound of the optimal solution. This strategy is combined with a standard iterative convex-concave procedure to recover a stationary point of the original non-convex problem.Comment: Submitted to IEEE PES General Meeting 201

Constraining spatial variations of the fine-structure constant in symmetron models

We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations and theoretical models through their predictions on the statistics of the $\alpha$ variation. Here we apply it to the case of symmetron models. We find no indications of deviations from the standard behavior, with current data providing an upper limit to the strength of the symmetron coupling to gravity ($\log{\beta^2}<-0.9$) when this is the only free parameter, and not able to constrain the model when also the symmetry breaking scale factor $a_{SSB}$ is free to vary.Comment: Phys. Lett. B (in press