Particular Solutions in Bimetric Theory and Their Implications

Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. We study certain aspects of dynamics in this theory: (1) It is shown that if either of the metrics is an Einstein solution then the other is always forced to be Einstein, too. For a class of bimetric models this constraint is stronger and as soon as one metric is Einstein, the other metric is forced to be proportional to it. As a consequence, the models in this class avoid a branch of pathological solutions that exhibit determinant singularities or nonlinear ghosts. These constraints persists in a generalized form when sources are included, but are destroyed in the massive gravity limit of the theory. (2) For another class of bimetric models, we show the existence of solutions that do not admit a massive gravity limit. A bimetric model that could exhibit a nonlinear version of "partially massless" symmetry belongs to both these classes. It is argued that if such a model exits, its symmetry will not survive in the massive gravity limit.Comment: Latex, 18 pages. Published versio

Extended Weyl Invariance in a Bimetric Model and Partial Masslessness

We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to 10-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.Comment: Latex, 35 pages. Matches published versio

Structure of the ovaries of the Nimba otter shrew, Micropotamogale lamottei, and the Madagascar hedgehog tenrec, Echinops telfairi

The otter shrews are members of the subfamily Potamogalinae within the family Tenrecidae. No description of the ovaries of any member of this subfamily has been published previously. The lesser hedgehog tenrec, Echinops telfairi, is a member of the subfamily Tenrecinae of the same family and, although its ovaries have not been described, other members of this subfamily have been shown to have ovaries with non-antral follicles. Examination of these two species illustrated that non-antral follicles were characteristic of the ovaries of both species, as was clefting and lobulation of the ovaries. Juvenile otter shrews range from those with only small follicles in the cortex to those with 300- to 400-mu m follicles similar to those seen in non-pregnant and pregnant adults. As in other species, most of the growth of the oocyte occurred when follicles had one to two layers of granulosa cells. When larger follicles became atretic in the Nimba otter shrew, hypertrophy of the theca interna produced nodules of glandular interstitial tissue. In the tenrec, the hypertrophying theca interna cells in most large follicles appeared to undergo degeneration. Both species had some follicular fluid in the intercellular spaces between the more peripheral granulosa cells. It is suggested that this fluid could aid in separation of the cumulus from the remaining granulosa at ovulation. The protruding follicles in lobules and absence of a tunica albuginea might also facilitate ovulation of non-antral follicles. Ovaries with a thin-absent tunica albuginea and follicles with small-absent antra are widespread within both the Eulipotyphla and in the Afrosoricida, suggesting that such features may represent a primitive condition in ovarian development. Lobulated and deeply crypted ovaries are found in both groups but are not as common in the Eulipotyphla making inclusion of this feature as primitive more speculative. Copyright (C) 2005 S. Karger AG, Basel

Facilitating decision-making in agriculture by using a system of models

This article presents a deterministic farm-level model developed to link to an existing partial equilibrium sector-level model of the grain and livestock sectors of South Africa. The objective is to create a linked system of models consisting of a sector- and farm-level model with the capability to analyse the likely effects of changes in policies and markets at both the sector and representative farm level in South Africa. A representative farm in the Free State Province is used to validate the farm-level model. The farm-level model is used to simulate a baseline as well as two scenarios of the representative farm for the period 2003 to 2010. Results indicate that the farm-level model simulates the representative farm rather accurately compared to historical data. The baseline and scenario results indicate that the linked system of models can be useful for policy and business decision-makers to analyse the impact of change in policies and markets at both the sector- and farm level.Farm Management,

Fluorescein angiography compared to three-dimensional measurements by the retinal thickness analyzer in classic choroidal neovascularization

Purpose: To compare and correlate imaging of classic subfoveal choroidal neovascularization (CNV) with noninvasive 3-dimensional imaging by the retinal thickness analyzer (RTA) to conventional fluorescein angiography (FA). Methods: A total of 29 eyes of 29 consecutive patients with predominantly classic CNV eligible for photodynamic therapy underwent FA and RTA imaging. The FA dimensions of the CNV were measured independently by two graders. With the RTA, masked to FA the size of the CNV itself as imaged in 3-dimensional reconstruction, the size of significantly thickened retina overlying the CNV and the maximum retinal thickness were measured. Results: The mean diameter of the CNV determined from 3-dimensional RTA reconstructions showed an excellent correlation with measurements from FA (r = 0.91, p < 0.001). The area of retinal thickening was by a mean of 0.7 mm in diameter larger and correlated moderately well with the size of the CNV on FA (r = 0.65, p < 0.001). In contrast, there was no correlation between the absolute retinal thickness and the CNV size on FA. Conclusions: Noninvasive quantitative mapping of predominantly classic CNV by RTA is feasible and also allows 3-dimensional measurement of the lesion itself. The results correlate well with FA assessment but visualize different properties of the disease. Copyright (c) 2007 S. Karger AG, Basel

Ultrastable reference pulser for high-resolution spectrometers

Solid-state double-pulse generator for a high resolution semiconductor detector meets specific requirements for resolution /0.05 percent/, amplitude range /0.1-13 MeV/, and repetition rate /0.1-1000 pulses per second/. A tag pulse is generated in coincidence with each reference pulse

124-Color Super-resolution Imaging by Engineering DNA-PAINT Blinking Kinetics

Optical super-resolution techniques reach unprecedented spatial resolution down to a few nanometers. However, efficient multiplexing strategies for the simultaneous detection of hundreds of molecular species are still elusive. Here, we introduce an entirely new approach to multiplexed super-resolution microscopy by designing the blinking behavior of targets with engineered binding frequency and duration in DNA-PAINT. We assay this kinetic barcoding approach in silico and in vitro using DNA origami structures, show the applicability for multiplexed RNA and protein detection in cells, and finally experimentally demonstrate 124-plex super-resolution imaging within minutes.We thank Martin Spitaler and the imaging facility of the MPI of Biochemistry for confocal imaging support

Linear and nonlinear tails II: exact decay rates in spherical symmetry

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.Comment: 17 pages, 3 figures, 2 table

Asymptotics from scaling for nonlinear wave equations

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the late-time behavior of solutions of the nonlinear problem in timelike and null directions.Comment: 14 pages; minor changes (notation, typos