Embedding Four-directional Paths on Convex Point Sets

A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an \mbox{$n$-vertex} four-directional path $P$ on a set $S$ of $n$ points in the plane is a straight-line drawing of $P$ where each vertex of $P$ is mapped to a distinct point of $S$ and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.Comment: 11 pages, full conference version including all proof

Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity

We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puzzle.Comment: 12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing, Bordeaux, 201

A serendipitous all sky survey for bright objects in the outer solar system

We use seven yearʼs worth of observations from the Catalina Sky Survey and the Siding Spring Survey covering most of the northern and southern hemisphere at galactic latitudes higher than 20° to search for serendipitously imaged moving objects in the outer solar system. These slowly moving objects would appear as stationary transients in these fast cadence asteroids surveys, so we develop methods to discover objects in the outer solar system using individual observations spaced by months, rather than spaced by hours, as is typically done. While we independently discover eight known bright objects in the outer solar system, the faintest having $V=19.8\pm 0.1,$ no new objects are discovered. We find that the survey is nearly 100% efficient at detecting objects beyond 25 AU for $V\lesssim 19.1$ ($V\lesssim 18.6$ in the southern hemisphere) and that the probability that there is one or more remaining outer solar system object of this brightness left to be discovered in the unsurveyed regions of the galactic plane is approximately 32%

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

3D time-lapse imaging of polygonal patterned ground in the McMurdo dry valleys of Antarctica

We surveyed four sets of polygons at 0.5 m line spacing using 100 and 200 MHz antennas for 3D GPR imaging at two field locations in the McMurdo Dry Valleys of Antarctica, one in Victoria Valley and the other in Beacon Valley. The aim was to use 3D GPR and time-lapse 3D GPR to resolve subsurface structure and PPG process activity over the thaw season of polygonal patterned ground (PPG) in Antarctica. We applied migration and topographic corrections to the data sets before collating the data into 3D cubes. The subsurface structure can be analyzed using the processed profiles and resulting 3D data cubes. Signal was received down to 12 m (200 MHz) and 20 m (100 MHz) depth. Variations in salt concentrations, soil horizons and crack penetration may be interpreted using these data sets. The time-lapse images from Victoria Valley show reductions in signal through the season provisionally identified with changing quantities of free water and salts associated with PPG activity. The results show that 3D GPR allows the collection of valuable information about the subsurface structure and processes of PPG and provides a way to monitor changes in these processes as climatic conditions evolve

The Influence of grinding and wear on residual stress and strength of zirconia ceramics

The effect of grinding and wear on the strength and residual stress in Mg-PSZ and Y-TZP was studied. The grinding tests were performed with 2 different diamond wheels on Mg-PSZ and with 3 different wheels on Y-TZP. The wheels differed mainly in diamond grain size. Strength, residual stress, and phase content were measured after the grinding tests. The counter-material in the wear tests was a hardened steel. Wear tests were performed under ambient conditions and under various loads with water as lubricant. The strength of worn surfaces was measured. The grinding anal. of Mg-PSZ resulted in a clear and consistent picture of the relation between the surface treatment, strength, phase content, and residual stress. The same anal. of Y-TZP showed that this material is more complex than Mg-PSZ. The results of the wear tests show that the strength of worn Mg-PSZ is influenced by the development of residual stress due to wear testing. The results of the wear tests on Y-TZP showed that this material is more complicated, and that more research is required to explain the behavior of Y-TZP. [on SciFinder (R)