On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes

We prove that if every real belongs to a set generic extension of the constructible universe then every \Sigma_1^1 equivalence E on reals either admits a Delta_1^HC reduction to the equality on the set 2^{<\om_1} of all countable binary sequences, or continuously embeds E_0, the Vitali equivalence. The proofs are based on a topology generated by OD sets

The supernova/gamma-ray burst/jet connection

The observed association between supernovae and gamma-ray bursts represents a cornerstone in our understanding of the nature of gamma-ray bursts. The collapsar model provides a theoretical framework for this connection. A key element is the launch of a bi-polar jet (seen as a gamma-ray burst). The resulting hot cocoon disrupts the star while the 56Ni produced gives rise to radioactive heating of the ejecta, seen as a supernova. In this discussion paper I summarise the observational status of the supernova/gamma-ray burst connection in the context of the 'engine' picture of jet-driven supernovae and highlight SN 2012bz/GRB 120422A -- with its luminous supernova but intermediate high-energy luminosity -- as a possible transition object between low-luminosity and jet gamma-ray bursts. The jet channel for supernova explosions may provide new insight into supernova explosions in general.Comment: 11 pages, 4 figures, discussion paper for Royal Society Meeting on "New windows on transients across the universe", London 23-24 April 2012, eds. P. O'Brien, S. Smart

Protein evolution

Among the proteins that have evolved over hundreds of millions of years, with important roles in defence against invading micro-organisms, are the pentraxins. The two major members of the family are known as CRP and SAP, and they evolve due to mutations in the underlying DNA. The Study Group was asked to construct a model of this evolution in order to answer specific questions about the occurrences of these proteins in man and in the horseshoe crab

Aggregation of stochastic models

Dstl examines battle simulations based on stochastic evolution codes. One such code, known as SIMBAT (SIMple BATtle program) models the evolution of the battle as a sequence of turns in which the two sets of combating units move in a landscape. The units have objectives and act accordingly, they can acquire enemy units if lines-of-sight in the landscape permit this, and they can fire upon and disable enemy units with a certain probability. Based on the setting of a large number of parameters, and also on the outcome of pseudo-random decisions and engagements made in the course of the action, a final outcome of the battle is achieved. Figure 1 shows a SIMBAT screenshot. Figure 1: Screenshot from a SIMBAT battle. The setting is that of a ‘standard’ battle (see full report). The problem posed to the Study Group is the following: Is it possible to analyse and subsequently calculate a battle in terms of smaller subunits which can then be aggregated into the whole in a systematic fashion? This could potentially speed up the processing of a large number of simulations

Effective interactions for the nuclear shell model

Various perturbative and non-perturbative many-body techniques are discussed in this work. Especially, we will focus on the summation of so-called Parquet diagrams with emphasis on applications to finite nuclei. Here, the subset of two-body Parquet equations will be discussed. A practical implementation of the corresponding equations for studies of effective interactions for finite nuclei is outlined.Comment: 55 pages, latex, to appear in Advances in many-body theory, vol

The Fundamental Plane at z=0.18

We present preliminary results regarding the Fundamental Plane (FP) for galaxies in the two rich clusters Abell 665 and Abell 2218. Both clusters have a redshift of 0.18. We have compared the FP for A665 and A2218, and for the cluster CL0024+16 at z=0.39, with the FP for the Coma cluster. The scatter around the FP is similar for all four clusters. There may be indications that the slope of the FP is more shallow for the intermediate redshift clusters than for the Coma cluster. More complete samples of galaxies in intermediate redshift clusters are needed to map in detail the possible change of the slope as function of redshift. The mass-to-light (M/L) ratio as measured by the FP changes with redshift. At z=0.18 the M/L ratio (in Gunn r) is 16+-9% smaller than for the Coma cluster. Together with earlier results reported for CL0024+16 this implies that the M/L ratio changes with redshift as Delta log M/L_r ~ -0.4 Delta z. The results presented here are in agreement with passive evolution of a stellar population, which formed at a redshift larger than one. However, the possible presence of more recent bursts of star formation complicates the interpretation of the data.Comment: 10 pages, 5 figures included, LaTeX style lamuphys.sty To appear in the proceedings of the 3rd ESO-VLT Workshop Galaxy Scaling Relations, eds. da Costa et al., Springe

Star-Forming Regions near GRB 990123

We reduced the Hubble Space Telescope Space Telescope Imaging Spectrograph images of the gamma-ray burst GRB 990123 that were obtained on 8-9 February 1999 and find V_0 = 25.36 +/- 0.10, which corresponds to a flux of 0.258 +/- 0.023 micro-Jy for the optical transient 16.644 days after the burst's peak. The probable host galaxy has V_0 = 24.25 +/- 0.07 (= 0.716 +/- 0.046 micro-Jy) and the optical transient is located 0.65 arcseconds (= 5.5 kpc) south of the galaxy's nucleus. We fit and subtracted a scaled point-spread function to the optical transient and found evidence for three bright knots situated within 0.5 arcseconds (= 4.3 kpc) of the optical transient. Each knot has V_0 ~ 28.1 +/- 0.3, a rest-frame V-band luminosity of between approximately 5e8 L_Sun and 8e8 L_Sun, and a star-formation rate of at least 0.1-0.2 Solar masses per year. The knots are centrally concentrated with full-width at half-maximum of approximately 0.17 arcseconds (= 1.5 kpc). Their sizes and luminosities are consistent with their being star-forming regions. The optical transient is located 0.15 arcseconds (= 1.3 kpc) southeast of the centre of one of these knots.Comment: 4 pages, 2 figures, to appear in Astronomy & Astrophysics Letter