Unique Sink Orientations of Grids

We introduce unique sink orientations of grids as digraph models for many well-studied problems, including linear programming over products of simplices, generalized linear complementarity problems over P-matrices (PGLCP), and simple stochastic games. We investigate the combinatorial structure of such orientations and develop randomized algorithms for finding the sink. We show that the orientations arising from PGLCP satisfy the Holt-Klee condition known to hold for polytope digraphs, and we give the first expected linear-time algorithms for solving PGLCP with a fixed number of block

Properties of the Remnant Clockwise Disk of Young Stars in the Galactic Center

We present new kinematic measurements and modeling of a sample of 116 young stars in the central parsec of the Galaxy in order to investigate the properties of the young stellar disk. The measurements were derived from a combination of speckle and laser guide star adaptive optics imaging and integral field spectroscopy from the Keck telescopes. Compared to earlier disk studies, the most important kinematic measurement improvement is in the precision of the accelerations in the plane of the sky, which have a factor of six smaller uncertainties (~10 uas/yr/yr). We have also added the first radial velocity measurements for 8 young stars, increasing the sample at the largest radii (6"-12") by 25%. We derive the ensemble properties of the observed stars using Monte-Carlo simulations of mock data. There is one highly significant kinematic feature (~20 sigma), corresponding to the well-known clockwise disk, and no significant feature is detected at the location of the previously claimed counterclockwise disk. The true disk fraction is estimated to be ~20%, a factor of ~2.5 lower than previous claims, suggesting that we may be observing the remnant of what used to be a more densely populated stellar disk. The similarity in the kinematic properties of the B stars and the O/WR stars suggests a common star formation event. The intrinsic eccentricity distribution of the disk stars is unimodal, with an average value of = 0.27 +/- 0.07, which we show can be achieved through dynamical relaxation in an initially circular disk with a moderately top-heavy mass function.Comment: 65 pages, 22 figures, 8 tables, submitted to Ap

Mass Media and the Immigration Ban

Our Topic is the Immigration Ban Vs Mass Media, which will focus on the opinions of the ban and how media content can change the public\u27s opinion. The problem we are addressing is the tendency of the general public to form opinions without research or knowledge of the topic they are considering. Data collection through surveying students is the best way to examine our study because we get a diverse collection of opinions on our topic. Our groups is examining four classrooms with surveys, two in which we show video content and two without. Results will be shared at Scholars Week Exhibition