In this and two companion papers, we report on an extended empirical study of the simulated annealing approach to combinatorial optimization proposed by S. Kirkpatrick et al. That study investigated how best to adapt simulated annealing to particular problems and compared its performance to that of more traditional algorithms. This paper (Part I) discusses annealing and our parameterized generic implementation of it, describes how we adapted this generic algorithm to the graph partitioning problem, and reports how well it compared to standard algorithms like the Kernighan-Lin algorithm. (For sparse random graphs, it tended to outperform Kernighan-Lin as the number of vertices become large, even when its much greater running time was taken into account. It did not perform nearly so well, however, on graphs generated with a built-in geometric structure.) We also discuss how we went about optimizing our implementation, and describe the effects of changing the various annealing parameters or varying the basic annealing algorithm itself.

We present photometric and spectroscopic observations of SN 2007if, an overluminous (M V = −20.4), red (B − V = 0.16 at B-band maximum), slow-rising (t rise = 24 days) type Ia supernova (SN Ia) in a very faint (M g = −14.10) host galaxy. A spectrum at 5 days past B-band maximum light is a direct match to the super-Chandrasekhar-mass candidate SN Ia 2003fg, showing Si II and C II at ∼ 9000 km s −1 . A high signal-to-noise co-addition of the SN spectral time series reveals no Na I D absorption, suggesting negligible reddening in the host galaxy, and the late-time color evolution has the same slope as the Lira relation for normal SNe Ia. The ejecta appear to be well mixed, with no strong maximum in I-band and a diversity of iron-peak lines appearing in near-maximum-light spectra. SN 2007if also displays a plateau in the Si II velocity extending as late as +10 days, which we interpret as evidence for an overdense shell in the SN ejecta. We calculate the bolometric light curve of the SN and use it and the Si II velocity evolution to constrain the mass of the shell and the underlying SN ejecta, and demonstrate that SN 2007if is strongly inconsistent with a Chandrasekhar-mass scenario. Within the context of a "tamped detonation" model appropriate for double-degenerate mergers, and assuming no host extinction, we estimate the total mass of the system to be 2.4 ± 0.2 M ⊙ , with 1.6 ± 0.1 M ⊙ of 56 Ni and with 0.3-0.5 M ⊙ in the form of an envelope of unburned carbon/oxygen. Our modeling demonstrates that the kinematics of shell entrainment provide a more efficient mechanism than incomplete nuclear burning for producing the low velocities typical of super-Chandrasekhar-mass SNe Ia.

Context. Use of Type Ia supernovae (SNe Ia) as distance indicators has proven to be a powerful technique for measuring the darkenergy equation of state. However, recent studies have highlighted potential biases correlated with the global properties of their host galaxies, large enough to induce systematic errors into such cosmological measurements if not properly treated. Aims. We study the host galaxy regions in close proximity to SNe Ia in order to analyze relations between the properties of SN Ia events and environments where their progenitors most likely formed. In this paper we focus on local Hα emission as an indicator of young progenitor environments. Methods. The Nearby Supernova Factory has obtained flux-calibrated spectral timeseries for SNe Ia using integral field spectroscopy. These observations enabled the simultaneous measurement of the SN and its immediate vicinity. For 89 SNe Ia we measured or set limits on Hα emission, used as a tracer of ongoing star formation, within a 1 kpc radius around each SN. This constitutes the first direct study of the local environment for a large sample of SNe Ia with accurate luminosity, color, and stretch measurements. Results. Our local star formation measurements provide several critical new insights. We find that SNe Ia with local Hα emission are redder by 0.036 ± 0.017 mag, and that the previously noted correlation between stretch and host mass is driven entirely by the SNe Ia coming from locally passive environments, in particular at the low-stretch end. There is no such trend for SNe Ia in locally star-forming environments. Our most important finding is that the mean standardized brightness for SNe Ia with local Hα emission is 0.094 ± 0.031 mag fainter on average than for those without. This offset arises from a bimodal structure in the Hubble residuals, with one mode being shared by SNe Ia in all environments and the other one exclusive to SNe Ia in locally passive environments. This structure also explains the previously known host-mass bias. We combine the star formation dependence of this bimodality with the cosmic star formation rate to predict changes with redshift in the mean SN Ia brightness and the host-mass bias. The strong change predicted is confirmed using high-redshift SNe Ia from the literature. Conclusions. The environmental dependences in SN Ia Hubble residuals and color found here point to remaining systematic errors in the standardization of SNe Ia. In particular, the observed brightness offset associated with local Hα emission is predicted to cause a significant bias in current measurements of the dark energy equation of state. Recognition of these effects offers new opportunities to improve SNe Ia as cosmological probes. For instance, we note that the SNe Ia associated with local Hα emission are more homogeneous, resulting in a brightness dispersion of only 0.105 ± 0.012 mag. Key words. cosmology: observationsAppendix is available in electronic form at http://www.aanda.orgArticle published by EDP Sciences A66, page 1 of 17 A&A 560...

This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi for improving local optimization algorithms. Here we report on experiments at adapting simulated annealing to graph coloring and number partitioning, two problems for which local optimization had not previously been thought suitable. For graph coloring, we report on three simulated annealing schemes, all of which can dominate traditional techniques for certain types of graphs, at least when large amounts of computing time are available. For number partitioning, simulated annealing is not competitive with the differencing algorithm of N. Karmarkar and R. M. Karp, except on relatively small instances. Moreover, if running time is taken into account, natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based, in sharp contrast to the observed performance of annealing on other problems.

We examine the relationship between Type Ia Supernova (SN Ia) Hubble residuals and the properties of their host galaxies using a sample of 115 SNe Ia from the Nearby Supernova Factory (SNfactory). We use host galaxy stellar masses and specific star-formation rates fitted from photometry for all hosts, as well as gas-phase metallicities for a subset of 69 star-forming (non-AGN) hosts, to show that the SN Ia Hubble residuals correlate with each of these host properties. With these data we find new evidence for a correlation between SN Ia intrinsic color and host metallicity. When we combine our data with those of other published SN Ia surveys, we find the difference between mean SN Ia brightnesses in low and high mass hosts is 0.077 ± 0.014 mag. When viewed in narrow (0.2 dex) bins of host stellar mass, the data reveal apparent plateaus of Hubble residuals at high and low host masses with a rapid transition over a short mass range (9.8 ≤ log(M * /M ) ≤ 10.4). Although metallicity has been a favored interpretation for the origin of the Hubble residual trend with host mass, we illustrate how dust in star-forming galaxies and mean SN Ia progenitor age both evolve along the galaxy mass sequence, thereby presenting equally viable explanations for some or all of the observed SN Ia host bias.