Drawing Planar Graphs with Few Geometric Primitives

We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path with an arbitrary number of edges). Let $n$ denote the number of vertices of a graph. We show that trees can be drawn with $3n/4$ straight-line segments on a polynomial grid, and with $n/2$ straight-line segments on a quasi-polynomial grid. Further, we present an algorithm for drawing planar 3-trees with $(8n-17)/3$ segments on an $O(n)\times O(n^2)$ grid. This algorithm can also be used with a small modification to draw maximal outerplanar graphs with $3n/2$ edges on an $O(n)\times O(n^2)$ grid. We also study the problem of drawing maximal planar graphs with circular arcs and provide an algorithm to draw such graphs using only $(5n - 11)/3$ arcs. This is significantly smaller than the lower bound of $2n$ for line segments for a nontrivial graph class.Comment: Appeared at Proc. 43rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2017

Weather in stellar atmosphere: the dynamics of mercury clouds in alpha Andromedae

The formation of long-lasting structures at the surfaces of stars is commonly ascribed to the action of strong magnetic fields. This paradigm is supported by observations of evolving cool spots in the Sun and active late-type stars, and stationary chemical spots in the early-type magnetic stars. However, results of our seven-year monitoring of mercury spots in non-magnetic early-type star alpha Andromedae show that the picture of magnetically-driven structure formation is fundamentally incomplete. Using an indirect stellar surface mapping technique, we construct a series of 2-D images of starspots and discover a secular evolution of the mercury cloud cover in this star. This remarkable structure formation process, observed for the first time in any star, is plausibly attributed to a non-equilibrium, dynamical evolution of the heavy-element clouds created by atomic diffusion and may have the same underlying physics as the weather patterns on terrestrial and giant planets.Comment: 10 pages, 2 figures; to be published in Nature Physic

Automorphisms of graphs of cyclic splittings of free groups

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.Comment: 22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicat

Upregulation of the cell-cycle regulator RGC-32 in Epstein-Barr virus-immortalized cells

Epstein-Barr virus (EBV) is implicated in the pathogenesis of multiple human tumours of lymphoid and epithelial origin. The virus infects and immortalizes B cells establishing a persistent latent infection characterized by varying patterns of EBV latent gene expression (latency 0, I, II and III). The CDK1 activator, Response Gene to Complement-32 (RGC-32, C13ORF15), is overexpressed in colon, breast and ovarian cancer tissues and we have detected selective high-level RGC-32 protein expression in EBV-immortalized latency III cells. Significantly, we show that overexpression of RGC-32 in B cells is sufficient to disrupt G2 cell-cycle arrest consistent with activation of CDK1, implicating RGC-32 in the EBV transformation process. Surprisingly, RGC-32 mRNA is expressed at high levels in latency I Burkitt's lymphoma (BL) cells and in some EBV-negative BL cell-lines, although RGC-32 protein expression is not detectable. We show that RGC-32 mRNA expression is elevated in latency I cells due to transcriptional activation by high levels of the differentially expressed RUNX1c transcription factor. We found that proteosomal degradation or blocked cytoplasmic export of the RGC-32 message were not responsible for the lack of RGC-32 protein expression in latency I cells. Significantly, analysis of the ribosomal association of the RGC-32 mRNA in latency I and latency III cells revealed that RGC-32 transcripts were associated with multiple ribosomes in both cell-types implicating post-initiation translational repression mechanisms in the block to RGC-32 protein production in latency I cells. In summary, our results are the first to demonstrate RGC-32 protein upregulation in cells transformed by a human tumour virus and to identify post-initiation translational mechanisms as an expression control point for this key cell-cycle regulator

Building Babies - Chapter 16

In contrast to birds, male mammals rarely help to raise the offspring. Of all mammals, only among rodents, carnivores, and primates, males are sometimes intensively engaged in providing infant care (Kleiman and Malcolm 1981). Male caretaking of infants has long been recognized in nonhuman primates (Itani 1959). Given that infant care behavior can have a positive effect on the infant’s development, growth, well-being, or survival, why are male mammals not more frequently involved in “building babies”? We begin the chapter defining a few relevant terms and introducing the theory and hypotheses that have historically addressed the evolution of paternal care. We then review empirical findings on male care among primate taxa, before focusing, in the final section, on our own work on paternal care in South American owl monkeys (Aotus spp.). We conclude the chapter with some suggestions for future studies.Deutsche Forschungsgemeinschaft (HU 1746/2-1) Wenner-Gren Foundation, the L.S.B. Leakey Foundation, the National Geographic Society, the National Science Foundation (BCS-0621020), the University of Pennsylvania Research Foundation, the Zoological Society of San Dieg

X-Ray Spectroscopy of Stars

(abridged) Non-degenerate stars of essentially all spectral classes are soft X-ray sources. Low-mass stars on the cooler part of the main sequence and their pre-main sequence predecessors define the dominant stellar population in the galaxy by number. Their X-ray spectra are reminiscent, in the broadest sense, of X-ray spectra from the solar corona. X-ray emission from cool stars is indeed ascribed to magnetically trapped hot gas analogous to the solar coronal plasma. Coronal structure, its thermal stratification and geometric extent can be interpreted based on various spectral diagnostics. New features have been identified in pre-main sequence stars; some of these may be related to accretion shocks on the stellar surface, fluorescence on circumstellar disks due to X-ray irradiation, or shock heating in stellar outflows. Massive, hot stars clearly dominate the interaction with the galactic interstellar medium: they are the main sources of ionizing radiation, mechanical energy and chemical enrichment in galaxies. High-energy emission permits to probe some of the most important processes at work in these stars, and put constraints on their most peculiar feature: the stellar wind. Here, we review recent advances in our understanding of cool and hot stars through the study of X-ray spectra, in particular high-resolution spectra now available from XMM-Newton and Chandra. We address issues related to coronal structure, flares, the composition of coronal plasma, X-ray production in accretion streams and outflows, X-rays from single OB-type stars, massive binaries, magnetic hot objects and evolved WR stars.Comment: accepted for Astron. Astrophys. Rev., 98 journal pages, 30 figures (partly multiple); some corrections made after proof stag

Opportunities for Process Control and Quality Assurance Using Online NIR Analysis to a Continuous Wet Granulation Tableting Line

This paper investigates the application of online near-infrared measurements as a means to measure blend uniformity in a continuous tableting line. Underlying all the monitoring and control methods is the ability to measure key tablet properties online at a rate suitable for control purposes. The use of NIR to determine any deviations in blend uniformity is demonstrated by interpreting the relevant spectral signature allowing quantitative information to be acquired for process monitoring and quality assurance. In addition to demonstrating the functionality of the NIR probe, the practical issues arising in the application are discussed. The composition of the blend was measured using an NIR probe over a range of concentrations and the results were calculated comparing sub unit dose scale of scrutiny of small populations. This was compared with predicted product quality for whole tablets over the whole production period. This technique has demonstrated how data collected online can be used to successfully predict the quality of the whole production run for the purposes of real-time product quality assurance

Bank performance and executive pay: tournament or teamwork

We investigate the relationship between the dispersion of executive pay and bank performance/valuation by examining two competing theories, the tournament theory (hierarchical wage structure) and the equity fairness theory (compressed wage structure). The key variable of executive pay dispersion is measured using a hand-collected dataset composed of 63 banks from OECD countries and 29 banks from developing countries. The dataset covers the period 2004 to 2012. By combining and modifying a translog profit function and a pay-dispersion model, we are able to address the potential problems of relying on reduced-form estimation. In our subsample of developed and civil law countries, where bank performance is measured by either Tobin’s Q or by the price-to-book ratio, the overall impact of executive pay dispersion is mostly negative, and we find supporting evidence for the equity fairness theory, except for very high levels of dispersion. There is a non-linear effect, as banks perform best when there is either very low or very high executive pay dispersion. For developing country sample banks, greater executive pay dispersion has a negative impact on bank profit. In our subsample of common law countries, however, we find no evidence of a significant impact of executive pay dispersion on bank performance. We conclude that lower executive pay dispersion, a proxy for teamwork, is mostly effective in enhancing bank performance in a significant section of sample banks, i.e., civil law and developing countries