Comment on "Oxygen as a Site Specific Probe of the Structure of Water and Oxide Materials", PRL 107, 144501 (2011)

A recent paper by Zeidler et al. (PRL 107, 144501 (2011)) describes a neutron scattering experiment on water in which oxygen isotope substitution is successfully achieved for the first time. Differences between scattering patterns with different oxygen isotopes give a combination of the O-O and O-H (or O-D) structure factors, and the method elegantly minimizes some of the problematic inelasticity effects associated with neutron scattering from hydrogen. Particular conclusions of the new work are that the OH bond length in the light water molecule is about 0.005A longer than the same bond in heavy water, and that the hydrogen bond peaks in both liquids are at about the same position. Notwithstanding the substantial progress demonstrated by the new work, the comparison with our own results (PRL, 101, 065502 (2008)) by Zeidler et al. is in our opinion misleading.Comment: 2 pages, 1 figure

Numerical integration of one-loop Feynman diagrams for N-photon amplitudes

In the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order, one approach is to perform all of the integrations, including the virtual loop integration numerically. One would use a subtraction scheme that removes infrared and collinear divergences from the integrand in a style similar to that used for real emission graphs. Then one would perform the loop integration by Monte Carlo integration along with the integrations over final state momenta. In this paper, we have explored how one can perform the numerical integration. We have studied the N-photon scattering amplitude with a massless electron loop in order to have a case with a singular integrand that is not, however, so singular as to require the subtractions. We report results for N = 4, N = 5 with left-handed couplings, and N=6.Comment: 30 pages including 5 figures. This is a revised version that is close to the published versio

Vitamin K catabolite inhibition of ovariectomy-induced bone loss: Structure–activity relationship considerations

The potential benefit of vitamin K as a therapeutic in osteoporosis is controversial and the vitamin K regimen being used clinically (45 mg/day) employs doses that are many times higher than required to ensure maximal gamma‐carboxylation of the vitamin K‐dependent bone proteins. We therefore tested the hypothesis that vitamin K catabolites, 5‐carbon (CAN5C) and 7‐carbon carboxylic acid (CAN7C) aliphatic side‐chain derivatives of the naphthoquinone moiety exert an osteotrophic role consistent with the treatment of osteoporosis

General subtraction method for numerical calculation of one-loop QCD matrix elements

We present a subtraction scheme for eliminating the ultraviolet, soft, and collinear divergences in the numerical calculation of an arbitrary one-loop QCD amplitude with an arbitrary number of external legs. The subtractions consist of local counter terms in the space of the four-dimensional loop momentum. The ultraviolet subtraction terms reproduce MSbar renormalization. The key point in the method for the soft and collinear subtractions is that, although the subtraction terms are defined graph-by-graph and the matrix element is also calculated graph-by-graph, the sum over graphs of the integral of each the subtraction term can be evaluated analytically and provides the well known simple pole structure that arises from subtractions from real emission graphs, but with the opposite sign.Comment: 38 pages, 10 figures, axodraw styl

A republic of consumers: Jo Littler in discussion with Clive Barnett and Kate Soper

Clive Barnett is a human geographer at the Open University and is part of a team working on a project entitled ‘Governing the Subjects and Spaces of Ethical Consumption’. Kate Soper, a professor of philosophy and a cultural theorist based at London Metropolitan University, is working with Lyn Thomas on their ‘Alternative Hedonism and the Theory and Politics of Consumer Culture’ project.1 Jo Littler interviewed them both about the cultural and political implications of the expansion of green, ethical and anti-consumerism

Parametric analysis of the quality of single preemption schedules on three uniform parallel machines

For a scheduling problem to minimize the makespan on three uniform parallel machines we present a parametric analysis of the quality of a schedule with at most one preemption compared to the global optimal schedule with any number of preemptions. A tight bound is derived as a function of the relative speeds of the machines, provided that two of the machines have the same speed

Power of preemption on uniform parallel machines

For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2-1/m is tight. If the makespan of the optimal preemptive schedule is defined by the ratio of the total processing times of r < m longest jobs over the total speed of r fastest machines, we show that the tight bound on the power of preemption is 2-1/min{r,m-r}

On the relationship between instability and Lyapunov times for the 3-body problem

In this study we consider the relationship between the survival time and the Lyapunov time for 3-body systems. It is shown that the Sitnikov problem exhibits a two-part power law relationship as demonstrated previously for the general 3-body problem. Using an approximate Poincare map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the 3-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general 3-body problem.Comment: 9 pages, 19 figures, accepted for publication in MNRA