Cylindrical Superlens by a Coordinate Transformation

Cylinder-shaped perfect lens deduced from the coordinate transformation method is proposed. The previously reported perfect slab lens is noticed to be a limiting form of the cylindrical lens when the inner radius approaches infinity with respect to the lens thickness. Connaturality between a cylindrical lens and a slab lens is affirmed by comparing their eigenfield transfer functions. We numerically confirm the subwavelength focusing capability of such a cylindrical lens with consideration of material imperfection. Compared to a slab lens, a cylindrical lens has several advantages, including finiteness in cross-section, and ability in lensing with magnification or demagnification. Immediate applications of such a cylindrical lens can be in high-resolution imaging and lithography technologies. In addition, its invisibility property suggests that it may be valuable for non-invasive electromagnetic probing.Comment: Minor changes to conform with the published versio

Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills

Using cutting techniques we obtain the two-loop N=4 super-Yang-Mills helicity amplitudes for four-gluon scattering in terms of scalar integral functions. The N=4 amplitudes are considerably simpler than corresponding QCD amplitudes and therefore provide a testing ground for exploring two-loop amplitudes. The amplitudes are constructed directly in terms of gauge invariant quantities and therefore remain relatively compact throughout the calculation. We also present a conjecture for the leading color four-gluon amplitudes to all orders in the perturbative expansion.Comment: Latex, 13 pages, 9 figures, minor changes to signs in eq.(14

Modelling the consequences of targeted selective treatment strategies on performance and emergence of anthelmintic resistance amongst grazing calves

The development of anthelmintic resistance by helminths can be slowed by maintaining refugia on pasture or in untreated hosts. Targeted selective treatments (TST) may achieve this through the treatment only of individuals that would benefit most from anthelmintic, according to certain criteria. However TST consequences on cattle are uncertain, mainly due to difficulties of comparison between alternative strategies. We developed a mathematical model to compare: 1) the most ‘beneficial’ indicator for treatment selection and 2) the method of selection of calves exposed to Ostertagia ostertagi, i.e. treating a fixed percentage of the population with the lowest (or highest) indicator values versus treating individuals who exceed (or are below) a given indicator threshold. The indicators evaluated were average daily gain (ADG), faecal egg counts (FEC), plasma pepsinogen, combined FEC and plasma pepsinogen, versus random selection of individuals. Treatment success was assessed in terms of benefit per R (BPR), the ratio of average benefit in weight gain to change in frequency of resistance alleles R (relative to an untreated population). The optimal indicator in terms of BPR for fixed percentages of calves treated was plasma pepsinogen and the worst ADG; in the latter case treatment was applied to some individuals who were not in need of treatment. The reverse was found when calves were treated according to threshold criteria, with ADG being the best target indicator for treatment. This was also the most beneficial strategy overall, with a significantly higher BPR value than any other strategy, but its degree of success depended on the chosen threshold of the indicator. The study shows strong support for TST, with all strategies showing improvements on calves treated selectively, compared with whole-herd treatment at 3, 8, 13 weeks post-turnout. The developed model appeared capable of assessing the consequences of other TST strategies on calf populations

Multipartite entanglement in four-qubit cluster-class states

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation $E_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum states. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.Comment: 7 pages, 3 figs, version 3, some refs. are adde