The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

Six questions on the construction of ontologies in biomedicine

(Report assembled for the Workshop of the AMIA Working Group on Formal Biomedical Knowledge Representation in connection with AMIA Symposium, Washington DC, 2005.) Best practices in ontology building for biomedicine have been frequently discussed in recent years. However there is a range of seemingly disparate views represented by experts in the field. These views not only reflect the different uses to which ontologies are put, but also the experiences and disciplinary background of these experts themselves. We asked six questions related to biomedical ontologies to what we believe is a representative sample of ontologists in the biomedical field and came to a number conclusions which we believe can help provide an insight into the practical problems which ontology builders face today

Transverse Optical Mode Patterns for an RF Excited Ar-He-Xe Laser

Transverse optical modes for an RF excited Ar-He-Xe laser are studied both experimentally and theoretically. A diffraction model for a waveguide with a nonsaturable gain and refractive index gradients placed between two plane mirrors is formulated. The effects of gain and diffraction index gradients and of diffraction in free space are evaluated for typical experimental conditions. A direct comparison between theoretical mode patterns and experimentally measured ones at distances of 17 and 114 cm from the output mirror demonstrated a satisfactory agreement for various laser wavelengths and gas mixture composition

The symbiotic star CH Cygni – II. The ejecta from the 1998-2000 active phase

We present Hubble Space Telescope (HST) imaging, a Very Large Array (VLA) radio map (4.74 GHz), optical high-resolution (echelle) spectroscopy and UBV photoelectric photometry of the symbiotic star CH Cyg obtained during its 1998–2000 active phase. The HST imaging, taken during eclipse, shows the central stars are embedded in a nebula extending to 620 ± 150 au for a distance of 270 ± 66 pc. The inner nebula is strongly influenced by the onset of activity and associated outflow in 1998. The surface brightness contours of the contemporaneous radio VLA observation agree well with HST images. Photometric observations of the broad 1999 U-minimum suggest that it is due to the eclipse of the active hot component by the giant on the long-period (14.5 yr) outer orbit. We also find that the onset of the 1998 and the 1992 active periods occur at the same orbital phase of the inner binary. Spectroscopic observations reveal two types of outflow from the active star: a high-velocity (>1200 km s−1) hot star wind sporadically alternating with a more massive outflow indicated by P-Cygni-like profiles. We present evidence connecting the extended nebulosity with the high-velocity shocked outflow, and hence the activity in the central binary

The first evidence for multiple pulsation axes: a new roAp star in the Kepler field, KIC 10195926

We have discovered a new rapidly oscillating Ap star among the Kepler Mission target stars, KIC 10195926. This star shows two pulsation modes with periods that are amongst the longest known for roAp stars at 17.1 min and 18.1 min, indicating that the star is near the terminal age main sequence. The principal pulsation mode is an oblique dipole mode that shows a rotationally split frequency septuplet that provides information on the geometry of the mode. The secondary mode also appears to be a dipole mode with a rotationally split triplet, but we are able to show within the improved oblique pulsator model that these two modes cannot have the same axis of pulsation. This is the first time for any pulsating star that evidence has been found for separate pulsation axes for different modes. The two modes are separated in frequency by 55 microHz, which we model as the large separation. The star is an alpha^2 CVn spotted magnetic variable that shows a complex rotational light variation with a period of Prot = 5.68459 d. For the first time for any spotted magnetic star of the upper main sequence, we find clear evidence of light variation with a period of twice the rotation period; i.e. a subharmonic frequency of $\nu_{\rm rot}/2$. We propose that this and other subharmonics are the first observed manifestation of torsional modes in an roAp star. From high resolution spectra we determine Teff = 7400 K, log g = 3.6 and v sin i = 21 km/s. We have found a magnetic pulsation model with fundamental parameters close to these values that reproduces the rotational variations of the two obliquely pulsating modes with different pulsation axes. The star shows overabundances of the rare earth elements, but these are not as extreme as most other roAp stars. The spectrum is variable with rotation, indicating surface abundance patches.Comment: 17 pages; 16 figures; MNRA

The global distribution of Bacillus anthracis and associated anthrax risk to humans, livestock and wildlife.

Bacillus anthracis is a spore-forming, Gram-positive bacterium responsible for anthrax, an acute infection that most significantly affects grazing livestock and wild ungulates, but also poses a threat to human health. The geographic extent of B. anthracis is poorly understood, despite multi-decade research on anthrax epizootic and epidemic dynamics; many countries have limited or inadequate surveillance systems, even within known endemic regions. Here, we compile a global occurrence dataset of human, livestock and wildlife anthrax outbreaks. With these records, we use boosted regression trees to produce a map of the global distribution of B. anthracis as a proxy for anthrax risk. We estimate that 1.83 billion people (95% credible interval (CI): 0.59-4.16 billion) live within regions of anthrax risk, but most of that population faces little occupational exposure. More informatively, a global total of 63.8 million poor livestock keepers (95% CI: 17.5-168.6 million) and 1.1 billion livestock (95% CI: 0.4-2.3 billion) live within vulnerable regions. Human and livestock vulnerability are both concentrated in rural rainfed systems throughout arid and temperate land across Eurasia, Africa and North America. We conclude by mapping where anthrax risk could disrupt sensitive conservation efforts for wild ungulates that coincide with anthrax-prone landscapes

Distributed Testing of Excluded Subgraphs

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangles. Hence, in particular, testing whether a graph is K_4-free, and testing whether a graph is C_4-free can be done in a constant number of rounds (where K_k denotes the k-node clique, and C_k denotes the k-node cycle). On the other hand, we show that testing K_k-freeness and C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K_k-freeness and C_k-freeness in a constant number of rounds for k>4

Endomorphism algebras of Abelian varieties with special reference to superelliptic Jacobians

This is (mostly) a survey article. We use an information about Galois properties of points of small order on an Abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line

On certain other sets of integers

We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).Comment: 29 pp. Corrected typos. Added definitions for some non-standard notation and remarks on lower bound