Computing maximum cliques in B2B_2-EPG graphs

EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends. Epstein et al. showed in 2013 that computing a maximum clique in $B_1$-EPG graphs is polynomial. As remarked in [Heldt et al., 2014], when the number of bends is at least $4$, the class contains $2$-interval graphs for which computing a maximum clique is an NP-hard problem. The complexity status of the Maximum Clique problem remains open for $B_2$ and $B_3$-EPG graphs. In this paper, we show that we can compute a maximum clique in polynomial time in $B_2$-EPG graphs given a representation of the graph. Moreover, we show that a simple counting argument provides a ${2(k+1)}$-approximation for the coloring problem on $B_k$-EPG graphs without knowing the representation of the graph. It generalizes a result of [Epstein et al, 2013] on $B_1$-EPG graphs (where the representation was needed)

Extremal maps of the universal hyperbolic solenoid

We show that the set of points in the Teichmuller space of the universal hyperbolic solenoid which do not have a Teichmuller extremal representative is generic (that is, its complement is the set of the first kind in the sense of Baire). This is in sharp contrast with the Teichmuller space of a Riemann surface where at least an open, dense subset has Teichmuller extremal representatives. In addition, we provide a sufficient criteria for the existence of Teichmuller extremal representatives in the given homotopy class. These results indicate that there is an interesting theory of extremal (and uniquely extremal) quasiconformal mappings on hyperbolic solenoids.Comment: LaTeX, 15 page

Cost-effectiveness of treatments for superficial venous refluxin patients with chronic venous ulceration.

Background Venous leg ulcers impair quality of life significantly, with substantial costs to health services. The aim of this study was to estimate the cost‐effectiveness of interventional procedures alongside compression therapy versus compression therapy alone for the treatment of chronic venous leg ulceration. Methods A Markov decision analytical model was developed. The main outcome measures were quality‐adjusted life‐years (QALYs) and lifetime costs per patient, from the perspective of the UK National Health Service at 2015 prices. Resource use included the initial procedures, compression therapy, primary care and outpatient consultations. The interventional procedures included superficial venous surgery, endothermal ablation and ultrasound‐guided foam sclerotherapy (UGFS). The study population was patients with a chronic venous ulcer who were eligible for either compression therapy or an interventional procedure. Data were obtained from systematic review and meta‐analysis of RCTs. Results Surgery gained 0·112 (95 per cent c.i. −0·011 to 0·213) QALYs compared with compression therapy alone, with a difference in lifetime costs of €−1330 (−3570 to 1262). Given the expected savings in community care, the procedure would pay for itself within 4 years. There was insufficient evidence regarding endothermal ablation and UGFS to draw conclusions. Discussion This modelling study found surgery to be more effective and less costly than compression therapy alone. Further RCT evidence is required for both endothermal ablation and UGFS

The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation

Helmut Hofer introduced in '93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3--manifolds $(M,\xi)$ with $\pi_2(M) \ne 0$. We modify Hofer's argument to prove the Weinstein conjecture for some examples of higher dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has a closed contractible Reeb orbit.Comment: 11 pages, 2 figure

Pseudo-Riemannian geodesic foliations by circles

We investigate under which assumptions an orientable pseudo-Riemannian geodesic foliations by circles is generated by an $S^1$-action. We construct examples showing that, contrary to the Riemannian case, it is not always true. However, we prove that such an action always exists when the foliation does not contain lightlike leaves, i.e. a pseudo-Riemannian Wadsley's Theorem. As an application, we show that every Lorentzian surface all of whose spacelike/timelike geodesics are closed, is finitely covered by $S^1\times \R$. It follows that every Lorentzian surface contains a non-closed geodesic.Comment: 14 page

The role of the helicopter in transportation

A general overview is presented of the role that the helicopter plays in the current aviation scene with special emphasis on its use in the airport access function. Technological problems of present-day aircraft are discussed along with some plausible solutions. The economic and regulatory aspects of commercial helicopter operations are presented. Finally six commercial operations utilizing helicopters are reviewed and conditions that enhance the success of the helicopter in the airport access function are proposed

Liquid Crystal Polarimetry for Metastability Exchange Optical Pumping of 3He

We detail the design and operation of a compact, discharge light polarimeter for metastability exchange optical pumping of 3He gas near 1 torr under a low magnetic field. The nuclear polarization of 3He can be discerned from its electron polarization, measured via the circular polarization of 668 nm discharge light from an RF excitation. This apparatus measures the circular polarization of this very dim discharge light using a nematic liquid crystal wave retarder (LCR) and a high-gain, transimpedance amplified Si photodiode. We outline corrections required in such a measurement, and discuss contributions to its systematic error