The Lebesgue Universal Covering Problem

In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pal, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen's last reduction was microsopic: he claimed to remove an area of $6 \cdot 10^{-18}$, but we show that he actually removed an area of just $8 \cdot 10^{-21}$. In the following, with the help of Greg Egan, we find a new, smaller universal covering with area less than $0.8441153$. This reduces the area of the previous best universal covering by a whopping $2.2 \cdot 10^{-5}$.Comment: 11 pages, 5 jpeg figures, numerical errors correcte

The cry of the owl: investigating decision-making in a contemporary feature film

This article extends the traditions of style-based criticism through an encounter with the insights that can be gained from engaging with filmmakers at work. By bringing into relationship two things normally thought of as separate: production history and disinterested critical analysis, the discussion aims to extend the subjects which criticism can appreciate as well as providing some insights on the creative process. Drawing on close analysis, on observations made during fieldwork and on access to earlier cuts of the film, this article looks at a range of interrelated decision-making anchored by the reading of a particular sequence. The article examines changes the film underwent in the different stages of production, and some of the inventions deployed to ensure key themes and ideas remained in play, as other elements changed. It draws conclusions which reveal perspectives on the filmmaking process, on collaboration, and on the creative response to material realities. The article reveals elements of the complexity of the process of the construction of image and soundtrack, and extends the range of filmmakers’ choices which are part of a critical dialogue. Has a relationship to ‘Sleeping with half open eyes: dreams and realities in The Cry of the Owl’, Movie: A Journal of Film Criticism, 1, (2010) which provides a broader interpretative context for the enquiry

Sleeping with half open eyes: dreams and realities in The Cry of the Owl

This article is a close analysis of The Cry of the Owl (Thraves, 2009). It is also part of larger project to bring together traditions of detailed criticism with those of production history, which culminates in second article on the film due to be published in 2011. The detail of the argument concerns analysing a range of the film’s key signifying systems, with a particular interest in the way the film explores the gap between images / impressions and characters’ realities; engages in a complex way with generic traditions and modes of address; establishes complex patterns of connection and contrast through blocking, camera strategies and narrative structure

WHICH RETAIL FOOD SERVICES ARE CONSUMERS WILLING TO DO WITHOUT

Consumer/Household Economics,

Benchmark Calculations for Perchlorate from Three Human Cohorts

The presence of low concentrations of perchlorate in some drinking water sources has led to concern regarding potential effects on the thyroid. In a recently published report, the National Academy of Sciences indicated that the perchlorate dose required to cause hypothyroidism in adults would probably be > 0.40 mg/kg-day for months or longer. In this study, we calculated benchmark doses for perchlorate from thyroid-stimulating hormone (TSH) and free thyroxine (T(4)) serum indicators from two occupational cohorts with long-term exposure to perchlorate, and from a clinical study of volunteers exposed to perchlorate for 2 weeks. The benchmark dose for a particular serum indicator was defined as the dose predicted to cause an additional 5 or 10% of persons to have a serum measurement outside of the normal range. Using the data from the clinical study, we estimated the half-life of perchlorate in serum at 7.5 hr and the volume of distribution at 0.34 L/kg. Using these estimates and measurements of perchlorate in serum or urine, doses in the occupational cohorts were estimated and used in benchmark calculations. Because none of the three studies found a significant effect of perchlorate on TSH or free T(4), all of the benchmark dose estimates were indistinguishable from infinity. The lower 95% statistical confidence limits on benchmark doses estimated from a combined analysis of the two occupational studies ranged from 0.21 to 0.56 mg/kg-day for free T(4) index and from 0.36 to 0.92 mg/kg-day for TSH. Corresponding estimates from the short-term clinical study were within these ranges