On the cardinality of sumsets in torsion-free groups

Let $A, B$ be finite subsets of a torsion-free group $G$. We prove that for every positive integer $k$ there is a $c(k)$ such that if $|B|\ge c(k)$ then the inequality $|AB|\ge |A|+|B|+k$ holds unless a left translate of $A$ is contained in a cyclic subgroup. We obtain $c(k)<c_0k^{6}$ for arbitrary torsion-free groups, and $c(k)<c_0k^{3}$ for groups with the unique product property, where $c_0$ is an absolute constant. We give examples to show that $c(k)$ is at least quadratic in $k$

Selected papers from the 16th Annual Bio-Ontologies Special Interest Group Meeting

Copyright @ 2014 Soldatova et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Over the 16 years, the Bio-Ontologies SIG at ISMB has provided a forum for vibrant discussions of the latest and most innovative advances in the research area of bio-ontologies, its applications to biomedicine and more generally in the organisation, sharing and re-use of knowledge in biomedicine and the life sciences. The six papers selected for this supplement span a wide range of topics including: ontology-based data integration, ontology-based annotation of scientific literature, ontology and data model development, representation of scientific results and gene candidate prediction

Adaptation to Health States: A Micro-Econometric Approach

Health care funding decisions in the UK are based on valuations of the general public. However, it has been shown that there is a disparity between a hypothetical valuation of the impact of a specific condition on health and the effect of that health state by someone who experiences it. This paper examines the issue of adaptation to health states, which partially may explain the discrepancy between hypothetical and experienced health state valuations. We use the British Cohort Study (BCS70) which is a longitudinal dataset that tracks a sample of British individuals since their birth in 1970. We use four BCS70 waves containing information on self-assessed health (SAH), morbidity as well as a number of socio-economic characteristics. To estimate the issue of adaptation, we implement a dynamic ordered probit model that controls for (health) state dependence. The empirical specification controls for morbidity and also includes a variable for the duration of the illness. We find that, for most chronic conditions, duration has a positive impact on self-assessed health, while for some conditions-such as diabetes- this does not occur. We interpret our results as evidence in support of the hypothesis that adaptation to chronic diseases exists and may explain at least in part the differences between general public and patients’ health state valuations

On the evolution of the molecular line profiles induced by the propagation of C-shock waves

We present the first results of the expected variations of the molecular line emission arising from material recently affected by C-shocks (shock precursors). Our parametric model of the structure of C-shocks has been coupled with a radiative transfer code to calculate the molecular excitation and line profiles of shock tracers such as SiO, and of ion and neutral molecules such as H13CO+ and HN13C, as the shock propagates through the unperturbed medium. Our results show that the SiO emission arising from the early stage of the magnetic precursor typically has very narrow line profiles slightly shifted in velocity with respect to the ambient cloud. This narrow emission is generated in the region where the bulk of the ion fluid has already slipped to larger velocities in the precursor as observed toward the young L1448-mm outflow. This strongly suggests that the detection of narrow SiO emission and of an ion enhancement in young shocks, is produced by the magnetic precursor of C-shocks. In addition, our model shows that the different velocity components observed toward this outflow can be explained by the coexistence of different shocks at different evolutionary stages, within the same beam of the single-dish observations.Comment: 7 pages, 4 figures, accepted for publication in Ap

Self-avoiding walks on a bilayer Bethe lattice

We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment results for a model with interactions between monomers on first neighbor sites of different layers. The thermodynamic properties of the model are studied in the grand-canonical formalism and both layers are considered to be Cayley trees. In the core region of the trees, which we may call a bilayer Bethe lattice, we find a very rich phase diagram in the parameter space defined by the two activities of monomers and the Boltzmann factor associated to the interlayer interaction between bonds or monomers. Beside critical and coexistence surfaces, there are tricritical, bicritical and critical endpoint lines, as well as higher order multicritical points.Comment: 21 pages, 10 figures. Journal of Statistical Mechanics: Theory and Experiment (in press

Covariant density functional theory: The role of the pion

We investigate the role of the pion in Covariant Density Functional Theory. Starting from conventional Relativistic Mean Field (RMF) theory with a non-linear coupling of the $\sigma$-meson and without exchange terms we add pions with a pseudo-vector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the non-central contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.Comment: 12 pages, 5 figure