Irrational guards are sometimes needed

In this paper we study the art gallery problem, which is one of the fundamental problems in computational geometry. The objective is to place a minimum number of guards inside a simple polygon such that the guards together can see the whole polygon. We say that a guard at position $x$ sees a point $y$ if the line segment $xy$ is fully contained in the polygon. Despite an extensive study of the art gallery problem, it remained an open question whether there are polygons given by integer coordinates that require guard positions with irrational coordinates in any optimal solution. We give a positive answer to this question by constructing a monotone polygon with integer coordinates that can be guarded by three guards only when we allow to place the guards at points with irrational coordinates. Otherwise, four guards are needed. By extending this example, we show that for every $n$, there is polygon which can be guarded by $3n$ guards with irrational coordinates but need $4n$ guards if the coordinates have to be rational. Subsequently, we show that there are rectilinear polygons given by integer coordinates that require guards with irrational coordinates in any optimal solution.Comment: 18 pages 10 Figure

Pauli Paramagnetic Effects on Vortices in Superconducting TmNi2B2C

The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6 Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.Comment: 4 pages, 4 figure

High-threshold mechanosensitive ion channels blocked by a novel conopeptide mediate pressure-evoked pain

Little is known about the molecular basis of somatosensory mechanotransduction in mammals. We screened a library of peptide toxins for effects on mechanically activated currents in cultured dorsal root ganglion neurons. One conopeptide analogue, termed NMB-1 for noxious mechanosensation blocker 1, selectively inhibits (IC50 1 µM) sustained mechanically activated currents in a subset of sensory neurons. Biotinylated NMB-1 retains activity and binds selectively to peripherin-positive nociceptive sensory neurons. The selectivity of NMB-1 was confirmed by the fact that it has no inhibitory effects on voltage-gated sodium and calcium channels, or ligand-gated channels such as acid-sensing ion channels or TRPA1 channels. Conversely, the tarantula toxin, GsMTx-4, which inhibits stretch-activated ion channels, had no effects on mechanically activated currents in sensory neurons. In behavioral assays, NMB-1 inhibits responses only to high intensity, painful mechanical stimulation and has no effects on low intensity mechanical stimulation or thermosensation. Unexpectedly, NMB-1 was found to also be an inhibitor of rapid FM1-43 loading (a measure of mechanotransduction) in cochlear hair cells. These data demonstrate that pharmacologically distinct channels respond to distinct types of mechanical stimuli and suggest that mechanically activated sustained currents underlie noxious mechanosensation. NMB-1 thus provides a novel diagnostic tool for the molecular definition of channels involved in hearing and pressure-evoked pain

Fermi surface and order parameter driven vortex lattice structure transitions in twin-free YBa2Cu3O7

We report on small-angle neutron scattering studies of the intrinsic vortex lattice (VL) structure in detwinned YBa2Cu3O7 at 2 K, and in fields up to 10.8 T. Because of the suppressed pinning to twin-domain boundaries, a new distorted hexagonal VL structure phase is stabilized at intermediate fields. It is separated from a low-field hexagonal phase of different orientation and distortion by a first-order transition at 2.0(2) T that is probably driven by Fermi surface effects. We argue that another first-order transition at 6.7(2) T, into a rhombic structure with a distortion of opposite sign, marks a crossover from a regime where Fermi surface anisotropy is dominant, to one where the VL structure and distortion is controlled by the order-parameter anisotropy.Comment: 4 pages, 3 figures (2 color), minor change

Temperature Dependence of the Flux Line Lattice Transition into Square Symmetry in Superconducting LuNi2_2B2_2C

We have investigated the temperature dependence of the H || c flux line lattice structural phase transition from square to hexagonal symmetry, in the tetragonal superconductor LuNi_2B_2C (T_c = 16.6 K). At temperatures below 10 K the transition onset field, H_2(T), is only weakly temperature dependent. Above 10 K, H_2(T) rises sharply, bending away from the upper critical field. This contradicts theoretical predictions of H_2(T) merging with the upper critical field, and suggests that just below the H_c2(T)-curve the flux line lattice might be hexagonal.Comment: 4 pages, 3 figure

Phonon-induced quadrupolar ordering of the magnetic superconductor TmNi2_2B2_2C

We present synchrotron x-ray diffraction studies revealing that the lattice of thulium borocarbide is distorted below T_Q = 13.5 K at zero field. T_Q increases and the amplitude of the displacements is drastically enhanced, by a factor of 10 at 60 kOe, when a magnetic field is applied along [100]. The distortion occurs at the same wave vector as the antiferromagnetic ordering induced by the a-axis field. A model is presented that accounts for the properties of the quadrupolar phase and explains the peculiar behavior of the antiferromagnetic ordering previously observed in this compound.Comment: submitted to PR

Design Aspects on Winding of an MgB₂ Superconducting Generator Coil

AbstractGenerators based on superconducting rotor coils are considered for future large off-shore wind turbines for their low weight and compact design, and for their possibility to reduce costs. In the 10-20 K temperature range, MgB2 superconductors carry current densities 100 times higher than standard copper conductors at room temperature at one tenth of the wire cost per unit carried current. In the framework of the European project INNWIND.EU, an MgB2 superconducting generator pole will be designed, built and tested. Some of the design aspects of this work with emphasis on the winding process and associated coil insulation are discussed. An overall high current density in the coil is of crucial importance to obtain clear benefits compared to conventional solutions. The wire itself may be the most important parameter in that respect. However, the overall current density of the coil is also influenced by the thickness of the turn-to-turn electrical insulation. Here we discuss the impact of the insulation and suggest the use of a one-step winding process, employing wet-winding, where the applied epoxy also constitutes the insulation layer between turns. In this way the coil is densified by approximately 10% compared to the use of an additional, dedicated, electrical insulation like Kapton for wet-winding or glass-fibre for dry-winding followed by vacuum impregnation. We show the results of a trial winding of 500 m of MgB2 superconducting wire into a double pancake coil using the wet-winding technique. The coil is tested for contacts between the turns to evaluate the suggested one-step wet-winding process

Vitamin D with Calcium reduces mortality: patient level pooled analysis of 70,528 patients from eight major vitamin D trials

Introduction: Vitamin D may affect multiple health outcomes. If so, an effect on mortality is to be expected. Using pooled data from randomized controlled trials, we performed individual patient data (IPD) and trial level meta-analyses to assess mortality among participants randomized to either vitamin D alone or vitamin D with calcium. Subjects and Methods: Through a systematic literature search, we identified 24 randomized controlled trials reporting data on mortality in which vitamin D was given either alone or with calcium. From a total of 13 trials with more than 1000 participants each, eight trials were included in our IPD analysis. Using a stratified Cox regression model, we calculated risk of death during 3 yr of treatment in an intention-to-treat analysis. Also, we performed a trial level meta-analysis including data from all studies. Results: The IPD analysis yielded data on 70,528 randomized participants (86.8% females) with a median age of 70 (interquartile range, 62–77) yr. Vitamin D with or without calcium reduced mortality by 7% [hazard ratio, 0.93; 95% confidence interval (CI), 0.88–0.99]. However, vitamin D alone did not affect mortality, but risk of death was reduced if vitamin D was given with calcium (hazard ratio, 0.91; 95% CI, 0.84–0.98). The number needed to treat with vitamin D plus calcium for 3 yr to prevent one death was 151. Trial level meta-analysis (24 trials with 88,097 participants) showed similar results, i.e. mortality was reduced with vitamin D plus calcium (odds ratio, 0.94; 95% CI, 0.88–0.99), but not with vitamin D alone (odds ratio, 0.98; 95% CI, 0.91–1.06). Conclusion: Vitamin D with calcium reduces mortality in the elderly, whereas available data do not support an effect of vitamin D alone

Patient level pooled analysis of 68,500 patients from seven major vitamin D fracture trials in the US and Europe

Objectives To identify participants’ characteristics that influence the anti-fracture efficacy of vitamin D or vitamin D plus calcium with respect to any fracture, hip fracture, and clinical vertebral fracture and to assess the influence of dosing regimens and co-administration of calcium. Design Individual patient data analysis using pooled data from randomised trials. Data sources Seven major randomised trials of vitamin D with calcium or vitamin D alone, yielding a total of 68 517 participants (mean age 69.9 years, range 47-107 years, 14.7% men). Study selection Studies included were randomised studies with at least one intervention arm in which vitamin D was given, fracture as an outcome, and at least 1000 participants. Data synthesis Logistic regression analysis was used to identify significant interaction terms, followed by Cox’s proportional hazards models incorporating age, sex, fracture history, and hormone therapy and bisphosphonate use. Results Trials using vitamin D with calcium showed a reduced overall risk of fracture (hazard ratio 0.92, 95% confidence interval 0.86 to 0.99, P=0.025) and hip fracture (all studies: 0.84, 0.70 to 1.01, P=0.07; studies using 10 μg of vitamin D given with calcium: 0.74, 0.60 to 0.91, P=0.005). For vitamin D alone in daily doses of 10 μg or 20 μg, no significant effects were found. No interaction was found between fracture history and treatment response, nor any interaction with age, sex, or hormone replacement therapy. Conclusion This individual patient data analysis indicates that vitamin D given alone in doses of 10-20 μg is not effective in preventing fractures. By contrast, calcium and vitamin D given together reduce hip fractures and total fractures, and probably vertebral fractures, irrespective of age, sex, or previous fractures.The WHI program is funded by the National Heart, Lung, and Blood Institute, National Institutes of Health, US Department of Health and Human Services through contracts N01WH22110, 24152, 32100-2, 32105-6, 32108-9, 32111-13, 32115, 32118-32119, 32122, 42107-26, 42129-32, and 44221. AA acknowledges personal funding from the UK Medical Research Council and Chief Scientist Office of the Scottish Government Health Directorates