Trajectory Visibility

We study the problem of testing whether there exists a time at which two entities moving along different piece-wise linear trajectories among polygonal obstacles are mutually visible. We study several variants, depending on whether or not the obstacles form a simple polygon, trajectories may intersect the polygon edges, and both or only one of the entities are moving. For constant complexity trajectories contained in a simple polygon with n vertices, we provide an (n) time algorithm to test if there is a time at which the entities can see each other. If the polygon contains holes, we present an (n log n) algorithm. We show that this is tight. We then consider storing the obstacles in a data structure, such that queries consisting of two line segments can be efficiently answered. We show that for all variants it is possible to answer queries in sublinear time using polynomial space and preprocessing time. As a critical intermediate step, we provide an efficient solution to a problem of independent interest: preprocess a convex polygon such that we can efficiently test intersection with a quadratic curve segment. If the obstacles form a simple polygon, this allows us to answer visibility queries in (n³/4log³ n) time using (nlog⁵ n) space. For more general obstacles the query time is (log^k n), for a constant but large value k, using (n^{3k}) space. We provide more efficient solutions when one of the entities remains stationary

Segment Visibility Counting Queries in Polygons

Let $P$ be a simple polygon with $n$ vertices, and let $A$ be a set of $m$ points or line segments inside $P$. We develop data structures that can efficiently count the number of objects from $A$ that are visible to a query point or a query segment. Our main aim is to obtain fast, $O(\mathop{\textrm{polylog}} nm$), query times, while using as little space as possible. In case the query is a single point, a simple visibility-polygon-based solution achieves $O(\log nm)$ query time using $O(nm^2)$ space. In case $A$ also contains only points, we present a smaller, $O(n + m^{2 + \varepsilon}\log n)$-space, data structure based on a hierarchical decomposition of the polygon. Building on these results, we tackle the case where the query is a line segment and $A$ contains only points. The main complication here is that the segment may intersect multiple regions of the polygon decomposition, and that a point may see multiple such pieces. Despite these issues, we show how to achieve $O(\log n\log nm)$ query time using only $O(nm^{2 + \varepsilon} + n^2)$ space. Finally, we show that we can even handle the case where the objects in $A$ are segments with the same bounds.Comment: 27 pages, 13 figure

Polls and the political process: the use of opinion polls by political parties and mass media organizations in European post‐communist societies (1990–95)

Opinion polling occupies a significant role within the political process of most liberal-capitalist societies, where it is used by governments, parties and the mass media alike. This paper examines the extent to which polls are used for the same purposes in the post-communist countries of Central and Eastern Europe, and in particular, for bringing political elites and citizens together. It argues that these political elites are more concerned with using opinion polls for gaining competitive advantage over their rivals and for reaffirming their political power, than for devolving political power to citizens and improving the general processes of democratization

The Robinson-Trautman Type III Prolongation Structure Contains K2_2

The minimal prolongation structure for the Robinson-Trautman equations of Petrov type III is shown to always include the infinite-dimensional, contragredient algebra, K$_2$, which is of infinite growth. Knowledge of faithful representations of this algebra would allow the determination of B\"acklund transformations to evolve new solutions.Comment: 20 pages, plain TeX, no figures, submitted to Commun. Math. Phy

Searching for dark galaxies: the AGES VC2 region

The VC2 strip (part of the AGES blind HI survey) spans 5x1 degrees of the Virgo Cluster, from the outskirts of the cluster to its interior. The strip covers part of subcluster A while avoiding the strong continuum source M87. 40 hours of observations were taken in January-February 2007 using the ALFA instrument on the Arecibo telescope, reaching a noise level as low as 0.5 mJy. For a 200 km/s velocity width, this gives a sensitivity limit of 6*10(6) Msolar at the Virgo distance (16 Mpc). Currently, 36 definite sources have been found, both by eye and with the automatic extractor Polyfind, with an additional 12 requiring follow-up observations, found only by one method

Targeting Superficial or Nodular Basal Cell Carcinoma with Topically Formulated Small Molecule Inhibitor of Smoothened

Purpose: Inappropriate activation of the Hedgehog (Hh) signaling pathway in skin is critical for the development of basal cell carcinomas (BCC). We have investigated the anti-BCC efficacy of topically-applied CUR61414, an inhibitor of the Hh signal transduction molecule Smoothened. Experimental Design: In preclinical studies, we used a depilatory model to evaluate the ability of topical formulations of CUR61414 to repress Hh responsive cells found at the base of hair follicles in normal skin. We also tested the in vivo effects of topical CUR61414 on murine BCCs developed in $Ptch1^{ +/−}$ K14-CreER2 p53 fl/fl mice. In a phase I clinical study, we evaluated the safety, tolerability, and efficacy of a multidose regimen of CUR61414 (0.09%, 0.35%, 1.1%, and 3.1%) applied topically to human superficial or nodular BCCs for up to 28 days. Results: In mice, topical CUR61414 significantly inhibited skin Hh signaling, blocked the induction of hair follicle anagen, and shrank existing BCCs. However, we observed no clinical activity of this formulation in human superficial or nodular BCCs in a phase I clinical study. Conclusions: Our data highlight some of the challenges of translating preclinical experience into successful human results for a topical anticancer agent.Stem Cell and Regenerative Biolog

AGES observations of Abell1367 and its outskirts

The Arecibo Galaxy Environment Survey (AGES, Auld et al. 2006) will map ~200 square degrees over the next years using the ALFA feed array at the 305-m Arecibo Telescope. AGES is specifically designed to investigate various galactic environments from local voids to interacting groups and cluster of galaxies. AGES will map 20 square degrees in the Coma-Abell1367 supercluster including the Abell cluster 1367 and its outskirts (up to ~2 virial radii). In Spring 2006 we nearly completed the observations of 5 square degrees in the range 11:34< RA< 11:54, 19:20<Dec<20:20 covering all the cluster core and part of its infalling region reaching a 5 sigma detection limit of M(HI)~4×10(8)Mxs2299 (assuming a velocity width ~200 km~s(−1)) at the distance of Abell1367 (~92 Mpc). An HI selected sample has been extracted from the datacube obtaining a catalogue of fluxes, recessional velocities, positions and velocity widths. We present a preliminary analysis of the properties of the HI sources and report the discovery of HI diffuse features within interacting groups at the periphery of Abell1367