Facets for Art Gallery Problems

The Art Gallery Problem (AGP) asks for placing a minimum number of stationary guards in a polygonal region P, such that all points in P are guarded. The problem is known to be NP-hard, and its inherent continuous structure (with both the set of points that need to be guarded and the set of points that can be used for guarding being uncountably infinite) makes it difficult to apply a straightforward formulation as an Integer Linear Program. We use an iterative primal-dual relaxation approach for solving AGP instances to optimality. At each stage, a pair of LP relaxations for a finite candidate subset of primal covering and dual packing constraints and variables is considered; these correspond to possible guard positions and points that are to be guarded. Particularly useful are cutting planes for eliminating fractional solutions. We identify two classes of facets, based on Edge Cover and Set Cover (SC) inequalities. Solving the separation problem for the latter is NP-complete, but exploiting the underlying geometric structure, we show that large subclasses of fractional SC solutions cannot occur for the AGP. This allows us to separate the relevant subset of facets in polynomial time. We also characterize all facets for finite AGP relaxations with coefficients in {0, 1, 2}. Finally, we demonstrate the practical usefulness of our approach. Our cutting plane technique yields a significant improvement in terms of speed and solution quality due to considerably reduced integrality gaps as compared to the approach by Kr\"oller et al.Comment: 29 pages, 18 figures, 1 tabl

Factors contributing to the time taken to consult with symptoms of lung cancer: a cross-sectional study

<b>Objectives</b>: To determine what factors are associated with the time people take to consult with symptoms of lung cancer, with a focus on those from rural and socially deprived areas. <b>Methods</b>: A cross-sectional quantitative interview survey was performed of 360 patients with newly diagnosed primary lung cancer in three Scottish hospitals (two in Glasgow, one in NE Scotland). Supplementary data were obtained from medical case notes. The main outcome measures were the number of days from (1) the date participant defined first symptom until date of presentation to a medical practitioner; and (2) the date of earliest symptom from a symptom checklist (derived from clinical guidelines) until date of presentation to a medical practitioner. <b>Results</b>: 179 participants (50%) had symptoms for more than 14 weeks before presenting to a medical practitioner (median 99 days; interquartile range 31–381). 270 participants (75%) had unrecognised symptoms of lung cancer. There were no significant differences in time taken to consult with symptoms of lung cancer between rural and/or deprived participants compared with urban and/or affluent participants. Factors independently associated with increased time before consulting about symptoms were living alone, a history of chronic obstructive pulmonary disease (COPD) and longer pack years of smoking. Haemoptysis, new onset of shortness of breath, cough and loss of appetite were significantly associated with earlier consulting, as were a history of chest infection and renal failure. <b>Conclusion</b>: For many people with lung cancer, regardless of location and socioeconomic status, the time between symptom onset and consultation was long enough to plausibly affect prognosis. Long-term smokers, those with COPD and/or those living alone are at particular risk of taking longer to consult with symptoms of lung cancer and practitioners should be alert to this

On the vanishing viscosity limit in a disk

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity)

Novel 1.5 GPa-strength with 50%-ductility by transformation-induced plasticity of non-recrystallized austenite in duplex steels

Needs for steel designs of ultra-high strength and excellent ductility have been an important issue in worldwide automotive industries to achieve energy conservation, improvement of safety, and crashworthiness qualities. Because of various drawbacks in existing 1.5-GPa-grade steels, new development of formable cold-rolled ultra-high-strength steels is essentially needed. Here we show a plausible method to achieve ultra-high strengths of 1.0~1.5 GPa together with excellent ductility above 50% by actively utilizing non-recrystallization region and TRansformation-Induced Plasticity (TRIP) mechanism in a cold-rolled and annealed Fe-Mn-Al-C-based steel. We adopt a duplex microstructure composed of austenite and ultra-fine ferrite in order to overcome low-yield-strength characteristics of austenite. Persistent elongation up to 50% as well as ultra-high yield strength over 1.4 GPa are attributed to well-balanced mechanical stability of non-crystallized austenite with critical strain for TRIP. Our results demonstrate how the non-recrystallized austenite can be a metamorphosis in 1.5-GPa-grade steel sheet design. ? 2017 The Author(s).114Ysciescopu

Nonequilibrium Green's function theory for transport and gain properties of quantum cascade structures

The transport and gain properties of quantum cascade (QC) structures are investigated using a nonequilibrium Green's function (NGF) theory which includes quantum effects beyond a Boltzmann transport description. In the NGF theory, we include interface roughness, impurity, and electron-phonon scattering processes within a self-consistent Born approximation, and electron-electron scattering in a mean-field approximation. With this theory we obtain a description of the nonequilibrium stationary state of QC structures under an applied bias, and hence we determine transport properties, such as the current-voltage characteristic of these structures. We define two contributions to the current, one contribution driven by the scattering-free part of the Hamiltonian, and the other driven by the scattering Hamiltonian. We find that the dominant part of the current in these structures, in contrast to simple superlattice structures, is governed mainly by the scattering Hamiltonian. In addition, by considering the linear response of the stationary state of the structure to an applied optical field, we determine the linear susceptibility, and hence the gain or absorption spectra of the structure. A comparison of the spectra obtained from the more rigorous NGF theory with simpler models shows that the spectra tend to be offset to higher values in the simpler theories.Comment: 44 pages, 16 figures, appearing in Physical Review B Dec 200

Non-Fermi liquid behavior and scaling of low frequency suppression in optical conductivity spectra of CaRuO3_3

Optical conductivity spectra $\sigma_1(\omega)$ of paramagnetic CaRuO$_3$ are investigated at various temperatures. At T=10 K, it shows a non-Fermi liquid behavior of $\sigma_1(\omega)\sim 1/{\omega}^{\frac 12}$, similar to the case of a ferromagnet SrRuO$_3$. As the temperature ($T$) is increased, on the other hand, $\sigma_1(\omega)$ in the low frequency region is progressively suppressed, deviating from the 1/{\omega}^{\frac 12%}-dependence. Interestingly, the suppression of $\sigma_1(\omega)$ is found to scale with $\omega /T$ at all temperatures. The origin of the $$ scaling behavior coupled with the non-Fermi liquid behavior is discussed.Comment: 4 pages, 3 figure

Functional consequences of Wnt-induced dishevelled 2 phosphorylation in canonical and non-canonical Wnt signaling

This research was originally published in Journal of Biological Chemitry. González-Sancho. Functional Consequences of Wnt-Induced Dishevelled2 Phosphorylation in Canonical and Non-Canonical Signaling. Journal of Biological Chemistry . 2013. 288 9428-9437 © the American Society for Biochemistry and Molecular BiologyEl título del postprint: Functional Consequences of Wnt-Induced Dishevelled2 Phosphorylation in Canonical and Non-Canonical SignalingDishevelled (Dvl) proteins are intracellular effectors of Wnt signaling that have essential roles in both canonical and noncanonical Wnt pathways. It has long been known that Wnts stimulate Dvl phosphorylation, but relatively little is known about its functional significance. We have previously reported that both Wnt3a and Wnt5a induce Dvl2 phosphorylation that is associated with an electrophoretic mobility shift and loss of recognition by monoclonal antibody 10B5. In the present study, we mapped the 10B5 epitope to a 16-amino acid segment of human Dvl2 (residues 594–609) that contains four Ser/Thr residues. Alanine substitution of these residues (P4m) eliminated the mobility shift induced by either Wnt3a or Wnt5a. The Dvl2 P4m mutant showed a modest increase in canonical Wnt/β-catenin signaling activity relative to wild type. Consistent with this finding, Dvl2 4Pm preferentially localized to cytoplasmic puncta. In contrast to wild-type Dvl2, however, the P4m mutant was unable to rescue Wnt3a-dependent neurite outgrowth in TC-32 cells following suppression of endogenous Dvl2/3. Earlier work has implicated casein kinase 1δ/ϵ as responsible for the Dvl mobility shift, and a CK1δ in vitro kinase assay confirmed that Ser594, Thr595, and Ser597 of Dvl2 are CK1 targets. Alanine substitution of these three residues was sufficient to abrogate the Wnt-dependent mobility shift. Thus, we have identified a cluster of Ser/Thr residues in the C-terminal domain of Dvl2 that are Wnt-induced phosphorylation (WIP) sites. Our results indicate that phosphorylation at the WIP sites reduces Dvl accumulation in puncta and attenuates β-catenin signaling, whereas it enables noncanonical signaling that is required for neurite outgrowth.This work was supported, in whole or in part, by National Institutes of Health Grant R01 CA123238 (to A. M. C. B.) and Postdoctoral Fellowship F32 CA117662 (to C. L. A.). This work was also supported by a fellowship from the Ministerio de Educación, Cultura, y Deportes, of Spain (to J. M. G.-S.), by New York State Department of Health postdoctoral Fellowship NYS C021339 (to Y. T.), and by charitable donations to Strang Cancer Prevention Center. This research also was supported in part by the Intramural Research Program of the National Institutes of Health, National Cancer Institut

Spacetime quantization induced by axial currents

In the present contribution we show that the introduction of a conserved axial current in electrodynamics can explain the quantization of electric charge, inducing at the same time a dynamical quantization of spacetime.Comment: To appear in Chaos Solitons & Fractal

Cosmic microwave background and large scale structure limits on the interaction between dark matter and baryons

We study the effect on the cosmic microwave background (CMB) anisotropy and large scale structure (LSS) power spectrum of a scattering interaction between cold dark matter and baryons. This scattering alters the CMB anisotropy and LSS spectrum through momentum transfer between the cold dark matter particles and the baryons. We find that current CMB observations can put an upper limit on the scattering cross section which is comparable with or slightly stronger than previous disk heating constraints at masses greater than 1 GeV, and much stronger at smaller masses. When large-scale structure constraints are added to the CMB limits, our constraint is more stringent than this previous limit at all masses. In particular, a dark matter-baryon scattering cross section comparable to the ``Spergel-Steinhardt'' cross section is ruled out for dark matter mass greater than 1 GeV.Comment: 8 pages, 2 figures, use RevTeX4, submitted to PRD replaced with revised versio

Spin-Parity Analysis of the Centrally produced KsKs system at 800 GeV

Results are presented of the spin-parity analysis on a sample of centrally produced mesons in the reaction (p p -> p_{slow} K_s K_s p_{fast}) with 800 GeV protons on liquid hydrogen. The spin-parity analysis in the mass region between threshold and 1.58 GeV/c^2 shows that the (K_s K_s) system is produced mainly in S-wave. The f_0(1500) is clearly observed in this region. Above 1.58 GeV/c^2 two solutions are possible, one with mainly S-wave and another with mainly D-wave. This ambiguity prevents a unique determination of the spin of the f_J(1710) meson.Comment: 6 pages, including 6 figures. LaTex, uses 'espcrc2.sty'. To appear in LEAP'96 proceeding