Generic Encodings of Constructor Rewriting Systems

Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages, with the negation over patterns. We propose in this paper a concise and clear algorithm computing the difference over patterns which can be used to define generic encodings of constructor term rewriting systems with negation and order into classical term rewriting systems. As a direct consequence, established methods used for term rewriting systems can be applied to analyze properties of the extended systems. The approach can also be seen as a generic compiler which targets any language providing basic pattern matching primitives. The formalism provides also a new method for deciding if a set of patterns subsumes a given pattern and thus, for checking the presence of useless patterns or the completeness of a set of patterns.Comment: Added appendix with proofs and extended example

Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5

We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark energy equation of state parameter w. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters. We implement an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant w. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-z galaxies. Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae only; the parameter uncertainties are underestimated by 10%. The weak lensing field-to-field variance pointings is 5%-15% higher than that predicted from N-body simulations. We find no bias of the lensing signal at high redshift, within the framework of a simple model. Assuming a systematic underestimation of the lensing signal at high redshift, the normalisation sigma_8 increases by up to 8%. Combining all three probes we obtain -0.10<1+w<0.06 at 68% confidence (-0.18<1+w<0.12 at 95%), including systematic errors. Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15sigma. [Abridged]Comment: 14 pages, 10 figures. Revised version, matches the one to be published in A&A. Modifications have been made corresponding to the referee's suggestions, including reordering of some section

Two superluminous supernovae from the early universe discovered by the Supernova Legacy Survey

We present spectra and lightcurves of SNLS 06D4eu and SNLS 07D2bv, two hydrogen-free superluminous supernovae discovered by the Supernova Legacy Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with a spectrum, at M_U = -22.7 is one of the most luminous SNe ever observed, and gives a rare glimpse into the restframe ultraviolet where these supernovae put out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but based on the supernova spectrum, we estimate it to be at z ~ 1.5. Both supernovae have similar observer-frame griz lightcurves, which map to restframe lightcurves in the U-band and UV, rising in ~ 20 restframe days or longer, and declining over a similar timescale. The lightcurves peak in the shortest wavelengths first, consistent with an expanding blackbody starting near 15,000 K and steadily declining in temperature. We compare the spectra to theoretical models, and identify lines of C II, C III, Fe III, and Mg II in the spectrum of SNLS 06D4eu and SCP 06F6, and find that they are consistent with an expanding explosion of only a few solar masses of carbon, oxygen, and other trace metals. Thus the progenitors appear to be related to those suspected for SNe Ic. A high kinetic energy, 10^52 ergs, is also favored. Normal mechanisms of powering core- collapse or thermonuclear supernovae do not seem to work for these supernovae. We consider models powered by 56Ni decay and interaction with circumstellar material, but find that the creation and spin-down of a magnetar with a period of 2ms, magnetic field of 2 x 10^14 Gauss, and a 3 solar mass progenitor provides the best fit to the data.Comment: ApJ, accepted, 43 pages, 15 figure

A Semi-Empirical Model of the Infra-Red Universe

We present a simple model of the infra-red universe, based as much as possible on local observations. We model the luminosity and number evolution of disk and starburst galaxies, including the effects of dust, gas and spectral evolution. Although simple, our approach is able to reproduce observations of galaxy number counts and the infra-red and sub-millimeter extra-galactic backgrounds. It provides a useful probe of galaxy formation and evolution out to high redshift. The model demonstrates the significant role of the starburst population and predicts high star formation rates at redshifts 3 to 4, consistent with recent extinction-corrected observations of Lyman break galaxies. Starbursting galaxies are predicted to dominate the current SCUBA surveys. Their star formation is driven predominantly by strong tidal interactions and mergers of galaxies. This leads to the creation of spheroidal stellar systems, which may act as the seeds for disk formation as gas infalls. We predict the present-day baryonic mass in bulges and halos is comparable to that in disks. From observations of the extra-galactic background, the model predicts that the vast majority of star formation in the Universe occurs at z<5.Comment: 23 pages including 9 figures. To appear in ApJ. Model results available electronically at http://astro.berkeley.edu/~jt/irmodel.htm

Type Ia Supernovae Rates and Galaxy Clustering from the CFHT Supernova Legacy Survey

The Canada-France-Hawaii Telescope Supernova Legacy Survey (SNLS) has created a large homogeneous database of intermediate redshift (0.2 < z < 1.0) type Ia supernovae (SNe Ia). The SNLS team has shown that correlations exist between SN Ia rates, properties, and host galaxy star formation rates. The SNLS SN Ia database has now been combined with a photometric redshift galaxy catalog and an optical galaxy cluster catalog to investigate the possible influence of galaxy clustering on the SN Ia rate, over and above the expected effect due to the dependence of SFR on clustering through the morphology-density relation. We identify three cluster SNe Ia, plus three additional possible cluster SNe Ia, and find the SN Ia rate per unit mass in clusters at intermediate redshifts is consistent with the rate per unit mass in field early-type galaxies and the SN Ia cluster rate from low redshift cluster targeted surveys. We also find the number of SNe Ia in cluster environments to be within a factor of two of expectations from the two component SNIa rate model.Comment: 21 pages, 2 figures, 6 tables, accepted for publication in A