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

Geometric Multicut

We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest “fence” F, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, where k is the number of different colors, as it can be seen as a geometric analogue to the well-studied multicut problem on graphs. We first give an O(n4log3n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colors and n corners in total. We then show that the problem is NP-hard for the case of three colors. Finally, we give a (2−4/3k)-approximation algorithm

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

Training and assessment of non-technical skills in Norwegian helicopter emergency services: a cross-sectional and longitudinal study

Background Deficient non-technical skills (NTS) among providers of critical care in helicopter emergency medical services (HEMS) is a threat to patient and operational safety. Skills can be improved through simulation-based training and assessment. A previous study indicated that physicians underwent less frequent training compared to pilots and HEMS crew members (HCM) and that all professional groups in Norwegian HEMS received limited training in how to cope with fatigue. Since then, training initiatives and a fatigue risk management project has been initiated. Our study aimed to explore if the frequency of simulation-based training and assessment of NTS in Norwegian HEMS has changed since 2011 following these measures. Methods A cross-sectional web-based survey from October through December 2016, of physicians, HCM and pilots from all civilian Norwegian HEMS-bases reporting the overall extent of simulation-based training and assessment of NTS. Results Of 214 invited, 109 responses were eligible for analysis. The frequency of simulation-based training and assessment of NTS has increased significantly for all professional groups in Norwegian HEMS, most prominently for the physicians. For all groups, the frequency of assessment is generally lower than the frequency of training. Conclusions Physicians in Norwegian HEMS seem to have adjusted to the NTS training culture of the other crew member groups. This might be a consequence of improved NTS training programs. The use of behavioural marker systems systematically in HEMS should be emphasized.publishedVersio

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

The three-dimensional prey field of the northern krill, Meganyctiphanes norvegica, and the escape responses of their copepod prey

In the north Atlantic, Meganyctiphanes norvegica feeds predominantly on copepods, including Calanus spp. To quantify its perceptual field for prey, and the sensory systems underlying prey detection, the responses of tethered krill to free-swimming Calanus spp. were observed in 3D using silhouette video imaging. An attack–which occurred despite the krill’s being tethered—was characterized by a pronounced movement of the krill’s antennae towards the target, followed by a propulsion and opening of the feeding basket. Frequency distributions of prey detection distances were significantly different in the light vs. the dark, with median values of 26.5 mm and 19.5 mm, respectively. There were no significant differences in the angles at which prey were detected by krill (relative to the predator’s longitudinal body axis) in the light vs. the dark. Prey detections were symmetrically distributed on either side of the predator, in both light and dark. However, significant asymmetry was found in the dorsal–ventral direction with 80% of the prey detections located below the midline of the krill’s body axis and, given the placement and orientation of the compound eyes, presumably outside its visual field of view. This indicates that, at least under these conditions, vision was not the main sensory modality involved in the detection of active prey by M. norvegica. However, under some circumstances, vision may provide supplemental information. Avoidance responses of copepod prey were nearly twice the velocity of their nominal background swimming speed (153 ± 48 and 85 ± 75 mm s−1, respectively), on average taking them 43 ± 16 mm away from the predator. This is far beyond the krill’s perceptual range, suggesting that the escape reaction provides an effective deterrent to predation (although perhaps less so for free-swimming krill). This information can be used to parameterize models that assess the role of krill as predators in marine ecosystems

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