Guarding curvilinear art galleries with edge or mobile guards via 2-dominance of triangulation graphs

AbstractIn this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polygons, i.e., polygons that are locally convex, except possibly at the vertices, and their edges are convex arcs.We transform the problem of monitoring a piecewise-convex polygon to the problem of 2-dominating a properly defined triangulation graph with edges or diagonals, where 2-dominance requires that every triangle in the triangulation graph has at least two of its vertices in its 2-dominating set. We show that: (1) ⌊n+13⌋ diagonal guards are always sufficient and sometimes necessary, and (2) ⌊2n+15⌋ edge guards are always sufficient and sometimes necessary, in order to 2-dominate a triangulation graph. Furthermore, we show how to compute: (1) a diagonal 2-dominating set of size ⌊n+13⌋ in linear time and space, (2) an edge 2-dominating set of size ⌊2n+15⌋ in O(n2) time and O(n) space, and (3) an edge 2-dominating set of size ⌊3n7⌋ in O(n) time and space.Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size ⌊n+13⌋ in O(nlogn) time, (2) an edge guard set of size ⌊2n+15⌋ in O(n2) time, and (3) an edge guard set of size ⌊3n7⌋ in O(nlogn) time. All space requirements are linear. Finally, we show that ⌊n3⌋ mobile or ⌈n3⌉ edge guards are sometimes necessary.When restricting our attention to monotone piecewise-convex polygons, the bounds mentioned above drop: ⌈n+14⌉ edge or mobile guards are always sufficient and sometimes necessary; such an edge or mobile guard set, of size at most ⌈n+14⌉, can be computed in O(n) time and space

Oscillation of differential systems of neutral type

summary:We study oscillatory properties of solutions of systems \[ \begin{aligned} {[y_1(t)-a(t)y_1(g(t))]}^{\prime }=&p_1(t)y_2(t), y_2^{\prime }(t)=&{-p_2}(t)f(y_1(h(t))), \quad t\ge t_0. \end{aligned} \

Testing limits to airflow perturbation device (APD) measurements

<p>Abstract</p> <p>Background</p> <p>The Airflow Perturbation Device (APD) is a lightweight, portable device that can be used to measure total respiratory resistance as well as inhalation and exhalation resistances. There is a need to determine limits to the accuracy of APD measurements for different conditions likely to occur: leaks around the mouthpiece, use of an oronasal mask, and the addition of resistance in the respiratory system. Also, there is a need for resistance measurements in patients who are ventilated.</p> <p>Method</p> <p>Ten subjects between the ages of 18 and 35 were tested for each station in the experiment. The first station involved testing the effects of leaks of known sizes on APD measurements. The second station tested the use of an oronasal mask used in conjunction with the APD during nose and mouth breathing. The third station tested the effects of two different resistances added in series with the APD mouthpiece. The fourth station tested the usage of a flexible ventilator tube in conjunction with the APD.</p> <p>Results</p> <p>All leaks reduced APD resistance measurement values. Leaks represented by two 3.2 mm diameter tubes reduced measured resistance by about 10% (4.2 cmH₂O·sec/L for control and 3.9 cm H₂O·sec/L for the leak). This was not statistically significant. Larger leaks given by 4.8 and 6.4 mm tubes reduced measurements significantly (3.4 and 3.0 cm cmH₂O·sec/L, respectively). Mouth resistance measured with a cardboard mouthpiece gave an APD measurement of 4.2 cm H₂O·sec/L and mouth resistance measured with an oronasal mask was 4.5 cm H₂O·sec/L; the two were not significantly different. Nose resistance measured with the oronasal mask was 7.6 cm H₂O·sec/L. Adding airflow resistances of 1.12 and 2.10 cm H₂O·sec/L to the breathing circuit between the mouth and APD yielded respiratory resistance values higher than the control by 0.7 and 2.0 cm H₂O·sec/L. Although breathing through a 52 cm length of flexible ventilator tubing reduced the APD measurement from 4.0 cm H₂O·sec/L for the control to 3.6 cm H₂O·sec/L for the tube, the difference was not statistically significant.</p> <p>Conclusion</p> <p>The APD can be adapted for use in ventilated, unconscious, and uncooperative patients with use of a ventilator tube and an oronasal mask without significantly affecting measurements. Adding a resistance in series with the APD mouthpiece has an additive effect on resistance measurements, and can be used for qualitative calibration. A leak size of at least the equivalent of two 3.2 mm diameter tubes can be tolerated without significantly affecting APD measurements.</p

A framework for remission in SLE: consensus findings from a large international task force on definitions of remission in SLE (DORIS)

Objectives Treat-to-target recommendations have identified 'remission' as a target in systemic lupus erythematosus (SLE), but recognise that there is no universally accepted definition for this. Therefore, we initiated a process to achieve consensus on potential definitions for remission in SLE. Methods An international task force of 60 specialists and patient representatives participated in preparatory exercises, a face-to-face meeting and follow-up electronic voting. The level for agreement was set at 90%. Results The task force agreed on eight key statements regarding remission in SLE and three principles to guide the further development of remission definitions: 1. Definitions of remission will be worded as follows: remission in SLE is a durable state characterised by . (reference to symptoms, signs, routine labs). 2. For defining remission, a validated index must be used, for example, clinical systemic lupus erythematosus disease activity index (SLEDAI)=0, British Isles lupus assessment group (BILAG) 2004 D/E only, clinical European consensus lupus outcome measure (ECLAM)=0; with routine laboratory assessments included, and supplemented with physician's global assessment. 3. Distinction is made between remission off and on therapy: remission off therapy requires the patient to be on no other treatment for SLE than maintenance antimalarials; and remission on therapy allows patients to be on stable maintenance antimalarials, low-dose corticosteroids (prednisone ≤5 mg/day), maintenance immunosuppressives and/or maintenance biologics. The task force also agreed that the most appropriate outcomes (dependent variables) for testing the prognostic value (construct validity) of potential remission definitions are: death, damage, flares and measures of health-related quality of life. Conclusions The work of this international task force provides a framework for testing different definitions of remission against long-term outcomes