A new approach to the assessment of lumen visibility of coronary artery stent at various heart rates using 64-slice MDCT

Coronary artery stent lumen visibility was assessed as a function of cardiac movement and temporal resolution with an automated objective method using an anthropomorphic moving heart phantom. Nine different coronary stents filled with contrast fluid and surrounded by fat were scanned using 64-slice multi-detector computed tomography (MDCT) at 50–100 beats/min with the moving heart phantom. Image quality was assessed by measuring in-stent CT attenuation and by a dedicated tool in the longitudinal and axial plane. Images were scored by CT attenuation and lumen visibility and compared with theoretical scoring to analyse the effect of multi-segment reconstruction (MSR). An average increase in CT attenuation of 144 ± 59 HU and average diminished lumen visibility of 29 ± 12% was observed at higher heart rates in both planes. A negative correlation between image quality and heart rate was non-significant for the majority of measurements (P > 0.06). No improvement of image quality was observed in using MSR. In conclusion, in-stent CT attenuation increases and lumen visibility decreases at increasing heart rate. Results obtained with the automated tool show similar behaviour compared with attenuation measurements. Cardiac movement during data acquisition causes approximately twice as much blurring compared with the influence of temporal resolution on image quality

Variations of the high-level Balmer line spectrum of the helium-strong star Sigma Orionis E

Using the high-level Balmer lines and continuum, we trace the density structure of two magnetospheric disk segments of the prototypical Bp star sigma Ori E (B2p) as these segments occult portions of the star during the rotational cycle. High-resolution spectra of the Balmer lines >H9 and Balmer edge were obtained on seven nights in January-February 2007 at an average sampling of 0.01 cycles. We measured equivalent width variations due to the star occultations by two disk segments 0.4 cycles apart and constructed differential spectra of the migrations of the corresponding absorptions across the Balmer line profiles. We first estimated the rotational and magnetic obliquity angles. We then simulated the observed Balmer jump variation using the model atmosphere codes synspec/circus and evaluated the disk geometry and gas thermodynamics. We find that the two occultations are caused by two disk segments. The first of these transits quickly, indicating that the segment resides in a range of distances, perhaps 2.5-6R_star, from the star. The second consists of a more slowly moving segment situated closer to the surface and causing two semi-resolved absorbing maxima. During its transit this segment brushes across the star's "lower" limb. Judging from the line visibility up to H23-H24 during the occultations, both disk segments have mean densities near 10^{12} cm^{-3} and are opaque in the lines and continuum. They have semiheights less than 1/2 of a stellar radius, and their temperatures are near 10500K and 12000K, respectively. In all, the disks of Bp stars have a much more complicated geometry than has been anticipated, as evidenced by their (sometimes) non-coplanarity, de-centerness, and from star to star, differences in disk height.Comment: Accepted by Astron. Astrophys, 13 pages, 4 embedded figure

Visibility Graphs, Dismantlability, and the Cops and Robbers Game

We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit-evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.Comment: 23 page

Trajectory Range Visibility

We study the problem of Trajectory Range Visibility, determining the sub-trajectories on which two moving entities become mutually visible. Specifically, we consider two moving entities with not necessarily equal velocities and moving on a given piece-wise linear trajectory inside a simple polygon. Deciding whether the entities can see one another with given constant velocities, and assuming the trajectories only as line segments, was solved by P. Eades et al. in 2020. However, we obtain stronger results and support queries on constant velocities for non-constant complexity trajectories. Namely, given a constant query velocity for a moving entity, we specify all visible parts of the other entity's trajectory and all possible constant velocities of the other entity to become visible. Regarding line-segment trajectories, we obtain $\mathcal{O}(n \log n)$ time to specify all pairs of mutually visible sub-trajectories s.t. $n$ is the number of vertices of the polygon. Moreover, our results for a restricted case on non-constant complexity trajectories yield $\mathcal{O}(n + m(\log m + \log n))$ time, in which $m$ is the overall number of vertices of both trajectories. Regarding the unrestricted case, we provide $\mathcal{O}(n \log n + m(\log m + \log n))$ running time. We offer $\mathcal{O}(\log n)$ query time for line segment trajectories and $\mathcal{O}(\log m + k)$ for the non-constant complexity ones s.t. $k$ is the number of velocity ranges reported in the answer. Interestingly, our results require only $\mathcal{O}(n + m)$ space for non-constant complexity trajectories

A Distributed Algorithm for Gathering Many Fat Mobile Robots in the Plane

In this work we consider the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting. Vision is the only mean of coordination. Using a state-machine representation we formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of robots. The main idea behind our algorithm is for the robots to reach a configuration in which all the following hold: (a) The robots' centers form a convex hull in which all robots are on the convex, (b) Each robot can see all other robots, and (c) The configuration is connected, that is, every robot touches another robot and all robots together form a connected formation. We show that starting from any initial configuration, the robots, making only local decisions and coordinate by vision, eventually reach such a configuration and terminate, yielding a solution to the gathering problem.Comment: 39 pages, 5 figure