Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Characterization of protection afforded by a bivalent virus-like particle vaccine against bluetongue virus serotypes 1 and 4 in sheep

BACKGROUND Bluetongue virus (BTV) is an economically important, arthropod borne, emerging pathogen in Europe, causing disease mainly in sheep and cattle. Routine vaccination for bluetongue would require the ability to distinguish between vaccinated and infected individuals (DIVA). Current vaccines are effective but are not DIVA. Virus-like particles (VLPs) are highly immunogenic structural mimics of virus particles, that only contain a subset of the proteins present in a natural infection. VLPs therefore offer the potential for the development of DIVA compatible bluetongue vaccines. METHODOLOGY/PRINCIPAL FINDINGS Merino sheep were vaccinated with either monovalent BTV-1 VLPs or a bivalent mixture of BTV-1 VLPs and BTV-4 VLPs, and challenged with virulent BTV-1 or BTV-4. Animals were monitored for clinical signs, antibody responses, and viral RNA. 19/20 animals vaccinated with BTV-1 VLPs either alone or in combination with BTV-4 VLPs developed neutralizing antibodies to BTV-1, and group specific antibodies to BTV VP7. The one animal that showed no detectable neutralizing antibodies, or group specific antibodies, had detectable viral RNA following challenge but did not display any clinical signs on challenge with virulent BTV-1. In contrast, all control animals' demonstrated classical clinical signs for bluetongue on challenge with the same virus. Six animals were vaccinated with bivalent vaccine and challenged with virulent BTV-4, two of these animals had detectable viral levels of viral RNA, and one of these showed clinical signs consistent with BTV infection and died. CONCLUSIONS There is good evidence that BTV-1 VLPs delivered as monovalent or bivalent immunogen protect from bluetongue disease on challenge with virulent BTV-1. However, it is possible that there is some interference in protective response for BTV-4 in the bivalent BTV-1 and BTV-4 VLP vaccine. This raises the question of whether all combinations of bivalent BTV vaccines are possible, or if immunodominance of particular serotypes could interfere with vaccine efficacy.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.