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

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

Light Curve Properties of Supernovae Associated With Gamma-ray Bursts

Little is known about the diversity in the light curves of GRB-SNe, including whether the light curve of SN 1998bw can be used as a representative template or whether there is a luminosity-decline rate relation akin to that of SNe Ia. In this paper, we aim to obtain well-constrained light curves of GRB-SNe without the assumption of empirical or parametric templates and to investigate whether the peak brightness correlates with other parameters such as the light curve shape or the time of peak. We select eight SNe in the redshift range 0.0085 to 0.606, which are firmly associated with GRBs. The light curves of these GRB-SNe are well sampled across the peak. Afterglow and host galaxy contributions are subtracted and dust reddening is corrected for. Low-order polynomial functions are fitted to the light curves. A K-correction is applied to transform the light curves into the rest frame V band. GRB-SNe follow a luminosity-decline rate relation similar to the Phillips relation for SNe Ia, with $M_{V,peak} = 1.59^{+0.28}_{-0.24} \Delta m_{V,15} - 20.61^{+0.19}_{-0.22}$, with $\chi^2 = 5.2$ for 6 dof and $M_{V,peak}$ and $\Delta m_{V,15}$ being the peak magnitude and decline rate in V band. This luminosity-decline rate relation is tighter than the k-s relation, where k and s are the factors describing the relative brightness and width to the light curve of SN 1998bw. The peak luminosities of GRB-SNe are also correlated with the time of peak: the brighter the GRB-SN, the longer the rise time. The light curve of SN 1998bw stretched around the time of explosion can be used as a template for GRB-SNe with reasonable confidence, but stretching around the peak produces better results. The existence of such a relation provides a new constraint on GRB explosion models. GRB-SNe can be used as standardizable candles to measure cosmological distances and constrain cosmological parameters.Comment: 17 pages, 15 figures. Submitted to Astronomy & Astrophysics on July 4, 201