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

Tabulator Redux: writing Into the Semantic Web

A first category of Semantic Web browsers were designed to present a given dataset (an RDF graph) for perusal, in various forms. These include mSpace, Exhibit, and to a certain extent Haystack. A second category tackled mechanisms and display issues around linked data gathered on the fly. These include Tabulator, Oink, Disco, Open Link Software's Data Browser, and Object Browser. The challenge of once that data is gathered, how might it be edited, extended and annotated has so far been left largely unaddressed. This is not surprising: there are a number of steep challenges for determining how to support editing information in the open web of linked data. These include the representation of both the web of documents and the web of things, and the relationships between them; ensuring the user is aware of and has control over the social context such as licensing and privacy of data being entered, and, on a web in which anyone can say anything about anything, helping the user intuitively select the things which they actually wish to see in a given situation. There is also the view update problem: the difficulty of reflecting user edits back through functions used to map web data to a screen presentation. In the latest version of the Tabulator project, described in this paper we have focused on providing the write side of the readable/writable web. Our approach has been to allow modification and addition of information naturally within the browsing interface, and to relay changes to the server triple by triple for least possible brittleness (there is no explicit 'save' operation). Challenges which remain include the propagation of changes by collaborators back to the interface to create a shared editing system. To support writing across (semantic) Web resources, our work has contributed several technologies, including a HTTP/SPARQL/Update-based protocol between an editor (or other system) and incrementally editable resources stored in an open source, world-writable 'data wiki'. This begins enabling the writable Semantic Web

Linked open government data: lessons from Data.gov.uk

The movement to publish government data is an opportunity to populate the linked data Web with data of good provenance. The benefits range from transparency to public service improvement, citizen engagement to the creation of social and economic value. There are many challenges to be met before the vision is implemented, and this paper describes the efforts of the EnAKTing project to extract value from data.gov.uk, through the stages of locating data sources, integrating data into the linked data Web, and browsing and querying it

Structure of the Coulomb and unitarity corrections to the cross section of e+e−e^+e^- pair production in ultra-relativistic nuclear collisions

We analyze the structure of the Coulomb and unitarity corrections to the single pair production as well as the cross section for the multiple pair production. In the external field approximation we consider the probability of $e^+e^-$ pair production at fixed impact parameter $\rho$ between colliding ultra-relativistic heavy nuclei. We obtain the analytical result for this probability at large $\rho$ as compared to the electron Compton wavelength. We estimate also the unitary corrections to the total cross section of the process.Comment: 10 pages, 2 figures, RevTeX, references correcte

Elastic neutron scattering in Quantum Critical Antiferromagnet Cr0.963_{0.963}V0.037_{0.037}

We have performed elastic neutron scattering studies of the quantum critical antiferromagnet Cr$_{0.963}$V$_{0.037}$. We have found that unlike pure Cr, which orders at two incommensurate wavevectors, Cr$_{0.963}$V$_{0.037}$ orders at four incommensurate and one commensurate wavevectors. We have found strong temperature dependent scattering at the commensurate and incommensurate wavevectors below 250 K. Results indicate that the primary effect of V doping on Cr is the modification of the nesting conditions of the Fermi surface and not the decreasing of the Neel temperature.Comment: 2 pages, 2 figures, submitted to SCES07 (to be published in Physica B), typos correcte

Supergravity Inflation on the Brane

We study N=1 Supergravity inflation in the context of the braneworld scenario. Particular attention is paid to the problem of the onset of inflation at sub-Planckian field values and the ensued inflationary observables. We find that the so-called $\eta$-problem encountered in supergravity inspired inflationary models can be solved in the context of the braneworld scenario, for some range of the parameters involved. Furthermore, we obtain an upper bound on the scale of the fifth dimension, M_5 \lsim 10^{-3} M_P, in case the inflationary potential is quadratic in the inflaton field, $\phi$. If the inflationary potential is cubic in $\phi$, consistency with observational data requires that $M_5 \simeq 9.2 \times 10^{-4} M_P$.Comment: 6 pages, 1 figure, to appear in Phys. Rev.

Narrowing of spectral lines beyond the natural or dephasing line width

Transient excitation and gated or delayed observation provides a narrowing of the inherent line width of the transition. Possible experimental one- and two-photon systems are discussed and the loss of signal with line narrowing is calculated. The general case of lines broadened by dephasing processes is treated. Contact is made with the line narrowing in recent Raman type experiments

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