Heuristics on pairing-friendly abelian varieties

We discuss heuristic asymptotic formulae for the number of pairing-friendly abelian varieties over prime fields, generalizing previous work of one of the authors arXiv:math1107.0307Comment: Pages 6-7 rewritten, other minor changes mad

Heuristics on pairing-friendly elliptic curves

We present a heuristic asymptotic formula as $x\to \infty$ for the number of isogeny classes of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value bounded by a fixed $\rho_0$ such that $1<\rho_0<2$, and with prime subgroup order at most $x$.Comment: text substantially rewritten, tables correcte

On the number of point of given order on odd degree hyperelliptic curves

For integers $N\geq 3$ and $g\geq 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.Comment: Example 5.6 of a modular curve added. A few minor corrections made. All comments welcome

Migration of human tympanic epithelium in health and disease

The gradual en masse migration of keratinised stratified squamous epithelium across the external surface of the human ear drum is an essential function in the maintenance of this delicate membrane by removing dead squamous epithelium to the external meatus for dispersal. The abnormal presence of the same epithelium in the middle ear space produces a proliferating, expanding mass which cannot escape from its enclosed environment. This condition, described as cholesteatoma*, can, in turn, invade the facial nerve, inner ear and intracranial contents and require surgical intervention which in itself poses some risk to the individual. The probable origins of cholesteatoma have been debated for more than a century. Two experiments are presented (1) to examine the morphology and structure of a whole, normal tympanic membrane and (2) to examine cultures of epithelium dissected from the neck of a cholesteatoma sac for differences in morphology and migration from those found in tympanic membrane epithelium, using light microscopy and time-lapse video recordings. The results show: (1) that the epithelial and fibroblast content can be determined in different layers of the whole tympanic membrane and that the close proximity and shared polarity between epithelium on the surface of the tympanic membrane and fibroblasts in the fibrous layer did not influence the direction of epithelial migration, (2) that in tissue culture, there are (a) marked differences in the yield of epithelium from explants dissected from the neck of a cholesteatoma sac, (b) that these cultures produce epithelium with morphological differences to tympanic membrane epithelium and (c) that fibroblasts affect the fate of epithelium during tissue culture. *cholesteatoma, first described by Cruveilhier (1829) as a pearly tumour of the temporal bone and a few years later (1838) by Johannes Muller

A novel method to characterise levels of pharmaceutical pollution in large-scale aquatic monitoring campaigns

Much of the current understanding of pharmaceutical pollution in the aquatic environment is based on research conducted in Europe, North America and other select high-income nations. One reason for this geographic disparity of data globally is the high cost and analytical intensity of the research, limiting accessibility to necessary equipment. To reduce the impact of such disparities, we present a novel method to support large-scale monitoring campaigns of pharmaceuticals at different geographical scales. The approach employs the use of a miniaturised sampling and shipping approach with a high throughput and fully validated direct-injection High-Performance Liquid Chromatography-Tandem Mass Spectrometry method for the quantification of 61 active pharmaceutical ingredients (APIs) and their metabolites in tap, surface, wastewater treatment plant (WWTP) influent and WWTP effluent water collected globally. A 7-day simulated shipping and sample stability assessment was undertaken demonstrating no significant degradation over the 1-3 days which is typical for global express shipping. Linearity (r 2 ) was consistently ≥0.93 (median = 0.99 ± 0.02), relative standard deviation of intra- and inter-day repeatability and precision was < 20% for 75% and 68% of the determinations made at three concentrations, respectively, and recovery from Liquid Chromatography Mass Spectrometry grade water, tap water, surface water and WWTP effluent were within an acceptable range of 60-130% for 87%, 76%, 77% and 63% of determination made at three concentrations respectively. Limits of detection and quantification were determined in all validated matrices and were consistently in the ng/L level needed for environmentally relevant API research. Independent validation of method results was obtained via an interlaboratory comparison of three surface-water samples and one WWTP effluent sample collected in North Liberty, Iowa (USA). Samples used for the interlaboratory validation were analysed at the University of York Centre of Excellence in Mass Spectrometry (York, UK) and the U.S. Geological Survey NationalWater Quality Laboratory in Denver (Colorado, USA). These results document the robustness of using this method on a global scale. Such application of this method would essentially eliminate the interlaboratory analytical variability typical of such large-scale datasets where multiple methods were used

Fate of Irgarol 1051, diuron and their main metabolites in two UK marine systems after restrictions in antifouling paints

Two major antifouling biocides used worldwide, Irgarol 1051 and diuron, and their degradation products in Shoreham Harbour and Brighton Marina, UK were studied during 2003-2004. The highest concentrations of Irgarol 1051 were 136 and 102 ng L(-1) in water and 40 and 49 ng g(-1) dry weight in sediments for Shoreham Harbour and Brighton Marina, respectively. As the degradation product of Irgarol 1051, M1 was also widespread, with the highest concentration of 59 ng L(-1) in water and 23 ng g(-1) in sediments in Shoreham Harbour, and 37 ng L(-1) in water and 5.6 ng g(-1) in sediments in Brighton Marina. The target compounds showed enhanced concentrations during the boating season (May-July), when boats were being re-painted (January-February), and where the density of pleasure crafts was high. Overall, the concentration of Irgarol 1051 decreased significantly from late 2000 to early 2004, indicating the effectiveness of controlling its concentrations in the marine environment following restricted use. Diuron was only detected in 14% of water samples, and mostly absent from sediment samples