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 $k$

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

A qualitative analysis of Sport Management interns’ perceptions of rotations in internships

The sport industry, which has evolved into a multi-billion rand industry, offers an increased number of complex and varied job opportunities. University Sport Management graduates are thus likely to face greater job demands in a highly competitive work environment. Rotations in Sport Management internships have been identified as an approach to prepare students for the job market. The purpose of this study was to ascertain the perceptions of Sport Management interns of rotations in internship. A qualitative case study research approach was used in the study. Eight semi-structured focus group interviews were conducted with Sport Management interns who completed their internship. The results of the study indicated that the positive experiences associated with the internship outweighed the negative experiences. Participants reported many benefits of rotations in internship. Among these were their experiences of different aspects of a sport organisation, exposure to different leadership styles, opportunity to apply their theoretical knowledge in the workplace, social issues in the workplace and development of different competencies. The findings also identified areas in which the internship experience could be strengthened. Given the great satisfaction experienced by interns, rotations in interns appear to be an ideal replacement to the traditional implementation of internship

A Learning Framework for Morphological Operators using Counter-Harmonic Mean

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1

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

Solution of a model of SAW's with multiple monomers per site on the Husimi lattice

We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers with one-site interactions only. We consider the version in which immediate self-reversals of the walk are forbidden (RF model). The phase diagram we obtain for the grand-canonical version of the model is similar to the one found in the solution of the Bethe lattice, with two distinct polymerized phases, a tricritical point and a critical endpoint.Comment: 16 pages, including 6 figure

Grand canonical and canonical solution of self-avoiding walks with up to three monomers per site on the Bethe lattice

We solve a model of polymers represented by self-avoiding walks on a lattice which may visit the same site up to three times in the grand-canonical formalism on the Bethe lattice. This may be a model for the collapse transition of polymers where only interactions between monomers at the same site are considered. The phase diagram of the model is very rich, displaying coexistence and critical surfaces, critical, critical endpoint and tricritical lines, as well as a multicritical point. From the grand-canonical results, we present an argument to obtain the properties of the model in the canonical ensemble, and compare our results with simulations in the literature. We do actually find extended and collapsed phases, but the transition between them, composed by a line of critical endpoints and a line of tricritical points, separated by the multicritical point, is always continuous. This result is at variance with the simulations for the model, which suggest that part of the line should be a discontinuous transition. Finally, we discuss the connection of the present model with the standard model for the collapse of polymers (self-avoiding self-attracting walks), where the transition between the extended and collapsed phases is a tricritical point.Comment: 34 pages, including 10 figure

Gas Kinematics and Excitation in the Filamentary IRDC G035.39-00.33

Some theories of dense molecular cloud formation involve dynamical environments driven by converging atomic flows or collisions between preexisting molecular clouds. The determination of the dynamics and physical conditions of the gas in clouds at the early stages of their evolution is essential to establish the dynamical imprints of such collisions, and to infer the processes involved in their formation. We present multi-transition 13CO and C18O maps toward the IRDC G035.39-00.33, believed to be at the earliest stages of evolution. The 13CO and C18O gas is distributed in three filaments (Filaments 1, 2 and 3), where the most massive cores are preferentially found at the intersecting regions between them. The filaments have a similar kinematic structure with smooth velocity gradients of ~0.4-0.8 km s-1 pc-1. Several scenarios are proposed to explain these gradients, including cloud rotation, gas accretion along the filaments, global gravitational collapse, and unresolved sub-filament structures. These results are complemented by HCO+, HNC, H13CO+ and HN13C single-pointing data to search for gas infall signatures. The 13CO and C18O gas motions are supersonic across G035.39-00.33, with the emission showing broader linewidths toward the edges of the IRDC. This could be due to energy dissipation at the densest regions in the cloud. The average H2 densities are ~5000-7000 cm-3, with Filaments 2 and 3 being denser and more massive than Filament 1. The C18O data unveils three regions with high CO depletion factors (f_D~5-12), similar to those found in massive starless cores.Comment: 20 pages, 14 figures, 6 tables, accepted for publication in MNRA

IC 4200: a gas-rich early-type galaxy formed via a major merger

We present the result of radio and optical observations of the S0 galaxy IC 4200. We find that the galaxy hosts 8.5 billion solar masses of HI rotating on a ~90 deg warped disk extended out to 60 kpc from the centre of the galaxy. Optical spectroscopy reveals a simple-stellar-population-equivalent age of 1.5 Gyr in the centre of the galaxy and V- and R-band images show stellar shells. Ionised gas is observed within the stellar body and is kinematically decoupled from the stars and characterised by LINER-like line ratios.We interpret these observational results as evidence for a major merger origin of IC 4200, and date the merger back to 1-3 Gyr ago.Comment: Accepted for publication in Astronomy & Astrophysics; 18 pages, 13 figures; the tables of Appendix C can be downloaded at http://www.astro.rug.nl/~pserra/IC420

Attribute Controlled Reconstruction and Adaptive Mathematical Morphology

ISBN : 978-3-642-38293-2International audienceIn this paper we present a reconstruction method controlled by the evolution of attributes. The process begins from a marker, propagated over increasing quasi-flat zones. The evolution of several increasing and non-increasing attributes is studied in order to select the appropriate region. Additionally, the combination of attributes can be used in a straightforward way. To demonstrate the performance of our method, three applications are presented. Firstly, our method successfully segments connected objects in range images. Secondly, input-adaptive structuring elements (SE) are defined computing the controlled propagation for each pixel on a pilot image. Finally, input-adaptive SE are used to assess shape features on the image. Our approach is multi-scale and auto-dual. Compared with other methods, it is based on a given attribute but does not require a size parameter in order to determine appropriate regions. It is useful to extract objects of a given shape. Additionally, our reconstruction is a connected operator since quasi-flat zones do not create new contours on the image