Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

Ultra-light Axions: Degeneracies with Massive Neutrinos and Forecasts for Future Cosmological Observations

A generic prediction of string theory is the existence of many axion fields. It has recently been argued that many of these fields should be light and, like the well known QCD axion, lead to observable cosmological consequences. In this paper we study in detail the effect of the so-called string axiverse on large scale structure, focusing on the morphology and evolution of density perturbations, anisotropies in the cosmic microwave background and weak gravitational lensing of distant galaxies. We quantify specific effects that will arise from the presence of the axionic fields and highlight possible degeneracies that may arise in the presence of massive neutrinos. We take particular care understanding the different physical effects and scales that come into play. We then forecast how the string axiverse may be constrained and show that with a combination of different observations, it should be possible to detect a fraction of ultralight axions to dark matter of a few percent.Comment: 24 pages, 16 figures, this version: corrected typos, some comments added, matches published versio

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

The ABCD of usability testing

We introduce a methodology for tracking and auditing feedback, errors and suggestions for software packages. This short paper describes how we innovate on the evaluation mechanism, introducing an (Antecedent, Barrier, Consequence and Development) ABCD form, embedded within an eParticipation platform to enable end users to easily report on any usability issues. This methodology will be utilised to improve the STEP cloud eParticipation platform (part of the current STEP Horizon2020 project http://step4youth.eu. The platform is currently being piloted in real life contexts, with the participation of public authorities that are integrating the eParticipation platform into their regular decision-making practices. The project is involving young people, through engagement and motivation strategies and giving them a voice in Environmental decision making at the local level. The pilot evaluation aims to demonstrate how open engagement needs to be embedded within public sector processes and the usability methodology reported here will help to identify the key barriers for wide scale deployment of the platform

A substantial prehistoric European ancestry amongst Ashkenazi maternal lineages

The origins of Ashkenazi Jews remain highly controversial. Like Judaism, mitochondrial DNA is passed along the maternal line. Its variation in the Ashkenazim is highly distinctive, with four major and numerous minor founders. However, due to their rarity in the general population, these founders have been difficult to trace to a source. Here we show that all four major founders, similar to 40% of Ashkenazi mtDNA variation, have ancestry in prehistoric Europe, rather than the Near East or Caucasus. Furthermore, most of the remaining minor founders share a similar deep European ancestry. Thus the great majority of Ashkenazi maternal lineages were not brought from the Levant, as commonly supposed, nor recruited in the Caucasus, as sometimes suggested, but assimilated within Europe. These results point to a significant role for the conversion of women in the formation of Ashkenazi communities, and provide the foundation for a detailed reconstruction of Ashkenazi genealogical history