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We show that a divergence-free measure on the plane is a continuous sum of unit tangent vector fields on rectifiable Jordan curves. This loop decomposition is more precise than the general decomposition in elementary solenoids given by S.K. Smirnov, when applied to the planar case. The proof involves extending the Fleming-Rishel formula to homogeneous BV functions (in any dimension), and establishing for such functions approximate continuity of measure theoretic connected components of suplevel sets as functions of the level. We apply these results to inverse potential problems whose source term is the divergence of some unknown (vector-valued) measure. A prototypical case is that of inverse magnetization problems when magnetizations are modeled by R3-valued Borel measures. We investigate methods for recovering a magnetization {\mu} by penalizing its measure theoretic total variation norm (TV). In particular, we prove that if a magnetization is supported in a plane, then TV-regularization schemes always have a unique minimizer, even in the presence of noise. It is further shown thatTV-norm minimization (among magnetizations generating the same field) uniquely recovers planar magnetizations in the following cases: when the magnetization is carried by a collection of sufficiently separated line segments and a set that is purely 1-unrectifiable, or when a superset of the support is tree-like. We note that such magnetizations can be recovered via TV-regularization schemes in the zero noise limit, by taking the regularization parameter to zero. This suggests definitions of sparsity in the present infinite dimensional context, that generate results akin to compressed sensing, Comment: 40 pages

We study inverse problems for the Poisson equation with source term the divergence of an R 3-valued measure; that is, the potential $Φ$ satisfies $∆Φ = div µ$, and $µ$ is to be reconstructed knowing (a component of) the field grad $Φ$ on a set dis-joint from the support of µ. Such problems arise in several electromagnetic contexts in the quasi-static regime, for instance when recovering a remanent magnetization from measurements of its magnetic field. We develop methods for recovering µ based on total variation regularization. We provide sufficient conditions for the unique recovery of µ, asymptotically when the regularization parameter and the noise tend to zero in a combined fashion, when it is uni-directional or when the magnetization has a support which is sparse in the sense that it is purely 1-unrectifiable. Numerical examples are provided to illustrate the main theoretical results.

Deadlock detection is a challenging issue in the analysis and design of on-chip networks. We have designed an algorithm to detect deadlocks automatically in on-chip networks with wormhole switching. The algorithm has been specified and proven correct in ACL2. To enable a top-down proof methodology, some parts of the algorithm have been left unimplemented. For these parts, the ACL2 specification contains constrained functions introduced with defun-sk. We used single-threaded objects to represent the data structures used by the algorithm. In this paper, we present details on the proof of correctness of the algorithm. The process of formal verification was crucial to get the algorithm flawless. Our ultimate objective is to have an efficient executable, and formally proven correct implementation of the algorithm running in ACL2., In Proceedings ACL2 2011, arXiv:1110.4473

We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on cardinality of codes with inner products in $[\ell,s]$ and lower bounds on the potential energy (for absolutely monotone interactions) for codes with inner products in $[\ell,1)$ (when the cardinality of the code is kept fixed) is revealed and explained. Thereby, we obtain a new extension of Levenshtein bounds for such codes. The universality of our bounds is exhibited by a unified derivation and their validity for a wide range of codes and potential functions., Comment: 18 pages, 1 figure

We investigate separation properties of $N$-point configurations that minimize discrete Riesz $s$-energy on a compact set $A\subset \mathbb{R}^p$. When $A$ is a smooth $(p-1)$-dimensional manifold without boundary and $s\in [p-2, p-1)$, we prove that the order of separation (as $N\to \infty$) is the best possible. The same conclusions hold for the points that are a fixed positive distance from the boundary of $A$ whenever $A$ is any $p$-dimensional set. These estimates extend a result of Dahlberg for certain smooth $(p-1)$-dimensional surfaces when $s=p-2$ (the harmonic case). Furthermore, we obtain the same separation results for `greedy' $s$-energy points. We deduce our results from an upper regularity property of the $s$-equilibrium measure (i.e., the measure that solves the continuous minimal Riesz $s$-energy problem), and we show that this property holds under a local smoothness assumption on the set $A$.

We study minimum energy problems relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, $\alpha\in(0,2]$, over signed Radon measures $\mu$ on $\mathbb R^n$, $n\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\mathbb R^n\setminus D$. We show that, though $A_2\cap\mathrm{Cl}_{\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\mu$ with $\mu^+\leqslant\xi$, where a constraint $\xi$ is properly chosen. We establish the sharpness of the sufficient conditions on the solvability thus obtained, provide descriptions of the weighted $\alpha$-Riesz potentials of the solutions, single out their characteristic properties, and analyze their supports. The approach developed is mainly based on the establishment of an intimate relationship between the constrained minimum $\alpha$-Riesz energy problem over signed measures associated with $(A_1,A_2)$ and the constrained minimum $\alpha$-Green energy problem over positive measures carried by $A_1$. The results are illustrated by examples., Comment: 30 pages

We study the constrained minimum energy problem with an external field relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$ for a generalized condenser $\mathbf A=(A_i)_{i\in I}$ in $\mathbb R^n$, $n\geqslant 3$, whose oppositely charged plates intersect each other over a set of zero capacity. Conditions sufficient for the existence of minimizers are found, and their uniqueness and vague compactness are studied. Conditions obtained are shown to be sharp. We also analyze continuity of the minimizers in the vague and strong topologies when the condenser and the constraint both vary, describe the weighted equilibrium vector potentials, and single out their characteristic properties. Our arguments are based particularly on the simultaneous use of the vague topology and a suitable semimetric structure on a set of vector measures associated with $\mathbf A$, and the establishment of completeness theorems for proper semimetric spaces. The results remain valid for the logarithmic kernel on $\mathbb R^2$ and $\mathbf A$ with compact $A_i$, $i\in I$. The study is illustrated by several examples., Comment: 3 figures

Data from multiple-sire beef cattle pastures have shown variability exists among the number of calves sired per bull. The reason(s) for the variability is unknown. Successful investigation of possible reasons requires accurate recording and evaluation of bull behavior. The purpose of this study was to assess the accuracy of classifying bull mounting events in a multiple-sire pasture using accelerometer data and classification algorithms., American Association of Bovine Practitioners Proceedings of the Annual Conference, 2016

We report measurements of ΩM, ΩΛ nd w from 11 supernovae (SNe) at z = 0.36-0.86 with high-quality light curves measured using WFPC2 on the Hubble Space Telescope (HST). This is an independent set of high-redshift SNe that confirms previous SN evidence for an accelerating universe. The high-quality light curves available from photometry on WFPC2 make it possible for these 11 SNe alone to provide measurements of the cosmological parameters comparable in statistical weight to the previous results. Combined with earlier Supernova Cosmology Project data, the new SNe yield a measurement of the mass density ΩM = 0.25 -0.06+0.07 (statistical) ± 0.04 (identified systematics), or equivalently, a cosmological constant of ± = 0.75 -0.07+0.06 (statistical) ± 0.04 (identified systematics), under the assumptions of a flat universe and that the dark energy equation-of-state parameter has a constant value w = -1. When the SN results are combined with independent flat-universe measurements of ΩM from cosmic microwave background and galaxy redshift distortion data, they provide a measurement of w = -1.05-0.20+0.15 (statistical) ± 0.09 (identified systematic), if w is assumed to be constant in time. In addition to high-precision light-curve measurements, the new data offer greatly improved color measurements of the high-redshift SNe and hence improved host galaxy extinction estimates. These extinction measurements show no anomalous negative E(B-V) at high redshift. The precision of the measurements is such that it is possible to perform a host galaxy extinction correction directly for individual SNe without any assumptions or priors on the parent E(B-V) distribution. Our cosmological fits using full extinction corrections confirm that dark energy is required with P(ΩΛ > 0) > 0.99, a result consistent with previous and current SN analyses that rely on the identification of a low-extinction subset or prior assumptions concerning the intrinsic extinction distribution.

For $s\geqslant d$, we obtain the leading term as $N\to \infty$ of the maximal weighted $N$-point Riesz $s$-polarization (or Chebyshev constant) for a certain class of $d$-rectifiable compact subsets of $\mathbb{R}^p$. This class includes compact subsets of $d$-dimensional $C^1$ manifolds whose boundary relative to the manifold has $\mathcal{H}_d$-measure zero, as well as finite unions of such sets when their pairwise intersections have $\mathcal{H}_d$-measure zero. We also explicitly find the weak$^*$ limit distribution of asymptotically optimal $N$-point polarization configurations as $N\to \infty$.

We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z < 0.35 nearby sample (8000 SNe), a 0.2 < z < 0.95 intermediate sample (8800 SNe), and a 0.75 < z < 1.55 high-z sample (1700 SNe). The nearby and intermediate surveys are assumed to be conducted from the ground, while the high-z is a joint ground- and space-based survey. This latter survey, the "Dark Energy Supernova Infra-Red Experiment" (DESIRE), is designed to fit within 6 months of Euclid observing time, with a dedicated observing programme. We simulate the SN events as they would be observed in rolling-search mode by the various instruments, and derive the quality of expected cosmological constraints. We account for known systematic uncertainties, in particular calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light curves. Using conservative assumptions and a 1D geometric Planck prior, we find that the ensemble of surveys would yield competitive constraints: a constant equation of stateparameter can be constrained to sigma(w) = 0.022, and a Dark Energy Task Force figure of merit of 203 is found for a two-parameter equation of state. Our simulations thus indicate that Euclid can bring a significant contribution to a purely geometrical cosmology constraint by extending a high-quality SN Ia Hubble diagram to z ~ 1.5. We also present other science topics enabled by the DESIRE Euclid observations.

For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field in the hypersingular case $ s\geq d$. Formulas for the weak$ ^* $ limit of normalized counting measures of such optimal point sets and the first-order asymptotic values of minimal energy are obtained. As an application, we derive a method for generating configurations whose normalized counting measures converge to a given absolutely continuous measure supported on a rectifiable subset of $ \mathbb{R}^{p} $. Results on separation and covering properties of discrete minimizers are given. Our theorems are illustrated with several numerical examples., Comment: Corrected typos; added references

There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties, separation, covering, and mesh ratio constants and present a new point set, equal area icosahedral points, with low mesh ratio. We analyze numerically the leading order asymptotics for the Riesz and logarithmic potential energy for these configurations with total points $N, 48 pages, 29 figures

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds are optimal for absolutely monotone potentials in the sense that for the linear programming technique they cannot be improved by using polynomials of the same or lower degree. When additional information about the structure (upper and lower bounds for the inner products) of the designs is known, improvements on the bounds are obtained. Furthermore, we provide `test functions' for determining when the linear programming lower bounds for energy can be improved utilizing higher degree polynomials. We also provide some asymptotic results for these energy bounds.

Reproductive performance and the number of calves produced by individual bulls within multiple-sire pastures has been shown to be highly variable. The objective of this project was to quantify patterns in the number of calves sired in multiple-sire pastures., American Association of Bovine Practitioners Proceedings of the Annual Conference, 2015

Contains fulltext : 91833.pdf (Author’s version preprint ) (Open Access)

Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the constrained settings, investigate the properties of minimizers, and prove their uniqueness. Furthermore, characterization theorems in terms of variational inequalities for the weighted potentials are established. The results obtained are illustrated by several examples., Comment: 32 pages, 1 figure

We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be improved by employing polynomials of the same or lower degrees in the Delsarte-Yudin method. However, improvements are sometimes possible and we provide a necessary and sufficient condition for the existence of such better bounds. All our bounds can be obtained in a unified manner that does not depend on the potential function, provided the potential is given by an absolutely monotone function of the inner product between pairs of points, and this is the reason for us to call them universal. We also establish a criterion for a given code of dimension $n$ and cardinality $N$ not to be LP-universally optimal, e.g. we show that two codes conjectured by Ballinger et al to be universally optimal are not LP-universally optimal., Comment: 25 pages, 3 figures, 3 tables

We fit the data for the binary-lens microlensing event MACHO 98-SMC-1 from 5 different microlensing collaborations and find two distinct solutions characterized by binary separation d and mass ratio q: (d,q)=(0.54,0.50) and (d,q)=(3.65,0.36), where d is in units of the Einstein radius. However, the relative proper motion of the lens is very similar in the two solutions, 1.30 km/s/kpc and 1.48 km/s/kpc, thus confirming that the lens is in the Small Magellanic Cloud. The close binary can be either rotating or approximately static but the wide binary must be rotating at close its maximum allowed rate to be consistent with all the data. We measure limb-darkening coefficients for five bands ranging from I to V. As expected, these progressively decrease with rising wavelength. This is the first measurement of limb darkening for a metal-poor A star., 29 pages + 9 figures + 2 tables, submitted to ApJ

Aims. We present cosmological constraints from a joint analysis of type Ia supernova (SN Ia) observations obtained by the SDSS-II and SNLS collaborations. The dataset includes several low-redshift samples (z < 0:1), all three seasons from the SDSS-II (0:05 < z < 0:4), and three years from SNLS (0:2 < z < 1), and it totals 740 spectroscopically confirmed type Ia supernovae with high-quality light curves. Methods. We followed the methods and assumptions of the SNLS three-year data analysis except for the following important improvements: 1) the addition of the full SDSS-II spectroscopically-confirmed SN Ia sample in both the training of the SALT2 light-curve model and in the Hubble diagram analysis (374 SNe); 2) intercalibration of the SNLS and SDSS surveys and reduced systematic uncertainties in the photometric calibration, performed blindly with respect to the cosmology analysis; and 3) a thorough investigation of systematic errors associated with the SALT2 modeling of SN Ia light curves. Results. We produce recalibrated SN Ia light curves and associated distances for the SDSS-II and SNLS samples. The large SDSS-II sample provides an eective, independent, low-z anchor for the Hubble diagram and reduces the systematic error from calibration systematics in the low-z SN sample. For a flat CDM cosmology, we find m = 0:295 0:034 (stat+sys), a value consistent with the most recent cosmic microwave background (CMB) measurement from the Planck and WMAP experiments. Our result is 1:8 (stat+sys) dierent than the previously published result of SNLS three-year data. The change is due primarily to improvements in the SNLS photometric calibration. When combined with CMB constraints, we measure a constant dark-energy equation of state parameter w = ?1:018 0:057 (stat+sys) for a flat universe. Adding baryon acoustic oscillation distance measurements gives similar constraints: w = ?1:0270:055. Our supernova measurements provide the most stringent constraints to date on the nature of dark energy.

Let $A$ be a compact $d$-rectifiable set embedded in Euclidean space $\RR^p$, $d\le p$. For a given continuous distribution $\sigma(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, our earlier results provided a method for generating $N$-point configurations on $A$ that have asymptotic distribution $\sigma (x)$ as $N\to \infty$; moreover such configurations are "quasi-uniform" in the sense that the ratio of the covering radius to the separation distance is bounded independent of $N$. The method is based upon minimizing the energy of $N$ particles constrained to $A$ interacting via a weighted power law potential $w(x,y)|x-y|^{-s}$, where $s>d$ is a fixed parameter and $w(x,y)=\left(\sigma(x)\sigma(y)\right)^{-({s}/{2d})}$. Here we show that one can generate points on $A$ with the above mentioned properties keeping in the energy sums only those pairs of points that are located at a distance of at most $r_N=C_N N^{-1/d}$ from each other, with $C_N$ being a positive sequence tending to infinity arbitrarily slowly. To do this we minimize the energy with respect to a varying truncated weight $v_N(x,y)=\Phi\(\left|x-y\right|/r_N\)w(x,y)$, where $\Phi:(0,\infty)\to [0,\infty)$ is a bounded function with $\Phi(t)=0$, $t\geq 1$, and $\lim_{t\to 0^+}\Phi(t)=1$. This reduces, under appropriate assumptions, the complexity of generating $N$ point `low energy' discretizations to order $N C_N^d$ computations.

In terms of the minimal $N$-point diameter $D_d(N)$ for $R^d,$ we determine, for a class of continuous real-valued functions $f$ on $[0,+\infty],$ the $N$-point $f$-best-packing constant $\min\{f(\|x-y\|)\, :\, x,y\in \R^d\}$, where the minimum is taken over point sets of cardinality $N.$ We also show that $$ N^{1/d}\Delta_d^{-1/d}-2\le D_d(N)\le N^{1/d}\Delta_d^{-1/d}, \quad N\ge 2,$$ where $\Delta_d$ is the maximal sphere packing density in $\R^d$. Further, we provide asymptotic estimates for the $f$-best-packing constants as $N\to\infty$.

We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in $\mathbb{R}^{d+1}$, $d\geq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\to \infty$) of the optimal $s$-energy.

For $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A,\rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\omega_N,A)$, which is the quotient of the covering radius of $\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\omega_N$. For best-packing configurations $\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s\to \infty$, we prove that $\gamma(\omega_N,A)\le 1$ and this bound can be attained even for the sphere. In the particular case when N=5 on $S^2$ with $\rho$ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega_5^*$, that is the limit (as $s\to \infty$) of 5-point $s$-energy minimizing configurations. Moreover, $\gamma(\omega_5^*,S^2)=1$.

We prove a conjecture of Ambrus, Ball and Erd\'{e}lyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form \sum_{k=1}^n f(d(z,z_k)), where $f:[0,\pi]\to [0,\infty]$ is non-increasing and strictly convex and $d(z,w)$ denotes the geodesic distance between $z$ and $w$ on the circle., Comment: 8 pages, 1 figure, to appear Discrete and Computational Geometry

We combine high redshift Type Ia supernovae from the first 3 years of the Supernova Legacy Survey (SNLS) with other supernova (SN) samples, primarily at lower redshifts, to form a high-quality joint sample of 472 SNe (123 low-$z$, 93 SDSS, 242 SNLS, and 14 {\it Hubble Space Telescope}). SN data alone require cosmic acceleration at >99.9% confidence, including systematic effects. For the dark energy equation of state parameter (assumed constant out to at least $z=1.4$) in a flat universe, we find $w = -0.91^{+0.16}_{-0.20}(\mathrm{stat}) ^{+0.07}_{-0.14} (\mathrm{sys})$ from SNe only, consistent with a cosmological constant. Our fits include a correction for the recently discovered relationship between host-galaxy mass and SN absolute brightness. We pay particular attention to systematic uncertainties, characterizing them using a systematics covariance matrix that incorporates the redshift dependence of these effects, as well as the shape-luminosity and color-luminosity relationships. Unlike previous work, we include the effects of systematic terms on the empirical light-curve models. The total systematic uncertainty is dominated by calibration terms. We describe how the systematic uncertainties can be reduced with soon to be available improved nearby and intermediate-redshift samples, particularly those calibrated onto USNO/SDSS-like systems., Published in ApJS. Data available from https://tspace.library.utoronto.ca/snls/

While it is generally accepted that Type Ia supernovae are the result of the explosion of a carbon-oxygen White Dwarf accreting mass in a binary system, the details of their genesis still elude us, and the nature of the binary companion is uncertain. Kasen (2010) points out that the presence of a non-degenerate companion in the progenitor system could leave an observable trace: a flux excess in the early rise portion of the lightcurve caused by the ejecta impact with the companion itself. This excess would be observable only under favorable viewing angles, and its intensity depends on the nature of the companion. We searched for the signature of a non-degenerate companion in three years of Supernova Legacy Survey data by generating synthetic lightcurves accounting for the effects of shocking and comparing true and synthetic time series with Kolmogorov-Smirnov tests. Our most constraining result comes from noting that the shocking effect is more prominent in rest-frame B than V band: we rule out a contribution from white dwarf-red giant binary systems to Type Ia supernova explosions greater than 10% at 2 sigma, and than 20% at 3 sigma level., Comment: 14 pages, 15 figures, resubmitted to ApJ, figure 15 modified

International audience; Precision cosmology with Type la supernovae (SNe Ia) makes use of the fact that SN Ia luminosities depend on their light-curve shapes and colours. Using Supernova Legacy Survey (SNLS) and other data, we show that there is an additional dependence on the global characteristics of their host galaxies: events of the same light-curve shape and colour are, on average, 0.08 mag (similar or equal to 4.0 sigma) brighter in massive host galaxies (presumably metal-rich) and galaxies with low specific star formation rates (sSFR). These trends do not depend on any assumed cosmological model, and are independent of the SN light-curve width: both fast and slow-declining events show the same trends. SNe Ia in galaxies with a low sSFR also have a smaller slope ('beta') between their luminosities and colours with similar to 2.7 sigma significance, and a smaller scatter on SN la Hubble diagrams (at 95 per cent confidence), though the significance of these effects is dependent on the reddest SNe. SN Ia colours are similar between low-mass and high-mass hosts, leading us to interpret their luminosity differences as an intrinsic property of the SNe and not of some external factor such as dust. If the host stellar mass is interpreted as a metallicity indicator using galaxy mass-metallicity relations, the luminosity trends are in qualitative agreement with theoretical predictions. We show that the average stellar mass, and therefore the average metallicity, of our SN Ia host galaxies decreases with redshift. The SN la luminosity differences consequently introduce a systematic error in cosmological analyses, comparable to the current statistical uncertainties on parameters such as in, the equation of state of dark energy. We show that the use of two SN Ia absolute magnitudes, one for events in high-mass (metal-rich) galaxies and the other for events in low-mass (metal-poor) galaxies, adequately corrects for the differences. Cosmological fits incorporating these terms give a significant reduction in chi(2) (3.8 sigma-4.5 sigma); linear corrections based on host parameters do not perform as well. We conclude that all future SN la cosmological analyses should use a correction of this (or similar) form to control demographic shifts in the underlying galaxy population.

GMOS optical long-slit spectroscopy at the Gemini-North telescope was used to classify targets from the Supernova Legacy Survey (SNLS) from July 2005 and May 2006 - May 2008. During this time, 95 objects were observed. Where possible the objects' redshifts (z) were measured from narrow emission or absorption features in the host galaxy spectrum, otherwise they were measured from the broader supernova features. We present spectra of 68 confirmed or probable SNe Ia from SNLS with redshifts in the range 0.17 \leq z \leq 1.02. In combination with earlier SNLS Gemini and VLT spectra, we used these new observations to measure pseudo-equivalent widths (EWs) of three spectral features - CaII H&K, SiII and MgII - in 144 objects and compared them to the EWs of low-redshift SNe Ia from a sample drawn from the literature. No signs of changes with z are seen for the CaII H&K and MgII features. Systematically lower EW SiII is seen at high redshift, but this can be explained by a change in demographics of the SNe Ia population within a two-component model combined with an observed correlation between EW SiII and photometric lightcurve stretch., 49 pages including 2 online-only appendices, accepted for publication in MNRAS

(Abridged) Precision cosmology with Type Ia supernovae (SNe Ia) makes use of the fact that SN Ia luminosities depend on their light-curve shapes and colours. Using Supernova Legacy Survey (SNLS) and other data, we show that there is an additional dependence on the global characteristics of their host galaxies: events of the same light-curve shape and colour are, on average, 0.08mag (~4.0sigma) brighter in massive host galaxies (presumably metal-rich) and galaxies with low specific star-formation rates (sSFR). SNe Ia in galaxies with a low sSFR also have a smaller slope ("beta") between their luminosities and colours with ~2.7sigma significance, and a smaller scatter on SN Ia Hubble diagrams (at 95% confidence), though the significance of these effects is dependent on the reddest SNe. SN Ia colours are similar between low-mass and high-mass hosts, leading us to interpret their luminosity differences as an intrinsic property of the SNe and not of some external factor such as dust. If the host stellar mass is interpreted as a metallicity indicator, the luminosity trends are in qualitative agreement with theoretical predictions. We show that the average stellar mass, and therefore the average metallicity, of our SN Ia host galaxies decreases with redshift. The SN Ia luminosity differences consequently introduce a systematic error in cosmological analyses, comparable to the current statistical uncertainties on parameters such as w. We show that the use of two SN Ia absolute magnitudes, one for events in high-mass (metal-rich) galaxies, and one for events in low-mass (metal-poor) galaxies, adequately corrects for the differences. Cosmological fits incorporating these terms give a significant reduction in chi^2 (3.8-4.5sigma). We conclude that future SN Ia cosmological analyses should use a correction of this (or similar) form to control demographic shifts in the galaxy population., Comment: Accepted for publication in MNRAS.

We present a method using the SALT2 light curve fitter to determine the redshift of Type Ia supernovae in the Supernova Legacy Survey (SNLS) based on their photometry in g', r', i' and z'. On 289 supernovae of the first three years of SNLS data, we obtain a precision $\sigma_{\Delta z/(1+z)} = 0.022$ on average up to a redshift of 1.0, with a higher precision of 0.016 for z0.45. The rate of events with $|\Delta z|/(1+z)>0.15$ (catastrophic errors) is 1.4%. Both the precision and the rate of catastrophic errors are better than what can be currently obtained using host galaxy photometric redshifts. Photometric redshifts of this precision may be useful for future experiments which aim to discover up to millions of supernovae Ia but without spectroscopy for most of them., Comment: 7 pages, 9 figures, published in Astronomy and Astrophysics

We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\sum_{j\neq k}f(d(\mathbf{x}_j, \mathbf{x}_k))$, where $d$ is the geodesic distance (with respect to $\Gamma$) between points on $\Gamma$. Completely monotonic functions, analytic kernel functions, Laurent series, and weighted kernel functions $f$ are studied. % Of particular interest are the geodesic Riesz potential $1/d^s$ ($s \neq 0$) and the geodesic logarithmic potential $\log(1/d)$. By analytic continuation we deduce the expansion for all complex values of $s$.

We have combined the large SN Ia database of the Canada-France-Hawaii Telescope Supernova Legacy Survey and catalogs of galaxies with photometric redshifts, VLA 1.4 GHz radio sources, and Spitzer infrared sources. We present eight SNe Ia in early-type host galaxies which have counterparts in the radio and infrared source catalogs. We find the SN Ia rate in subsets of radio and infrared early-type galaxies is ~1-5 times the rate in all early-type galaxies, and that any enhancement is always, Comment: 14 pages, 6 figures, 7 tables, accepted for publication in AJ

Let $A$ be a compact set in ${\mathbb R}^p$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^s$ is the unique Borel probability measure with support in $A$ that minimizes $$ I_s(\mu):=\iint\frac{1}{|x-y|^s}d\mu(y)d\mu(x)$$ over all such probability measures. If $A$ is strongly $({\mathcal H}^d, d)$-rectifiable, then $\mu^s$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below.

30 pags., 17 figs., 12 tabs. 4 apps., We present a new compilation of Type Ia supernovae (SNe Ia), a new data set of low-redshift nearby-Hubble-flow SNe, and new analysis procedures to work with these heterogeneous compilations. This >Union> compilation of 414 SNe Ia, which reduces to 307 SNe after selection cuts, includes the recent large samples of SNe Ia from the Supernova Legacy Survey and ESSENCE Survey, the older data sets, as well as the recently extended data set of distant supernovae observed with the Hubble Space Telescope (HST). A single, consistent, and blind analysis procedure is used for all the various SN Ia subsamples, and a new procedure is implemented that consistently weights the heterogeneous data sets and rejects outliers. We present the latest results from this Union compilation and discuss the cosmological constraints from this new compilation and its combination with other cosmological measurements (CMB and BAO). The constraint we obtain from supernovae on the dark energy density is ¿¿ = 0.713+ 0.027¿0.029(stat)+ 0.036¿0.039(sys) , for a flat, ¿CDM universe. Assuming a constant equation of state parameter, w, the combined constraints from SNe, BAO, and CMB give w = ¿ 0.969+ 0.059¿0.063(stat)+ 0.063¿0.066(sys) . While our results are consistent with a cosmological constant, we obtain only relatively weak constraints on a w that varies with redshift. In particular, the current SN data do not yet significantly constrain w at z > 1. With the addition of our new nearby Hubble-flow SNe Ia, these resulting cosmological constraints are currently the tightest available., This work was supported in part by the Director, Office of Science, Office of High Energy and Nuclear Physics, US Department of Energy, through contract DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under contract DEAC02- 05CH11231. The use of Portuguese time for the YALO telescope was supported by Fundacao para a Ciencia e Tecnologia, Portugal, and by Project PESO/ESO/P/PRO/1257/98. M. K. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG). P. E. N. acknowledges support from the USDepartment of Energy Scientific Discovery throughAdvanced Computing program under contract DE-FG02-06ER06-04. A.M. M. acknowledges financial support from Fundacao para a Ciencia e Tecnologia (FCT), Portugal, through project PESO/P/PRO/ 15139/99.

We present a measurement of the distant Type la supernova (SN Ia) rate derived from the first 2 yr of the Canada-France-Hawaii Telescope Supernova Legacy Survey. We observed four 1° × 1° fields with a typical temporal frequency of (Δt) ∼ 4 observer-frame days over time spans of 158-211 days per season for each field, with breaks during the full Moon. We used 8-10 m class telescopes for spectroscopic follow-up to confirm our candidates and determine their redshifts. Our starting sample consists of 73 spectroscopically verified SNe la in the redshift range 0.2 < z < 0.6. We derive a volumetric SN Ia rate of r V(〈z〉 = 0.47) = [0.42 0.090.13(syst.) ± 0.06(stat.)] × 10 -4 yr -1 Mpc 3, assuming h = 0.7, Ω m -0.3, and a flat cosmology. Using recently published galaxy luminosity functions derived in our redshift range, we derive a SN Ia rate per unit luminosity of r L(〈z〉 = 0.47) = 0.154 -0.0330.048(syst.) 0.0310.039(stat.) SN units. Using our rate alone, we place an upper limit on the component of SN la production that tracks the cosmic star formation history of 1 SN la per 10 3 M ⊙ of stars formed. Our rate and other rates from surveys using spectroscopic sample confirmation display only a modest evolution out to z = 0.55. © 2006. The American Astronomical Society. All rights reserved.

We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz $s$-energy configurations and determine the $s$-th root asymptotic behavior (as $s\to \infty)$ of the minimal energy constants. We show that the upper and the lower dimension of a set defined through the Riesz energy or best-packing coincides with the upper and lower Minkowski dimension, respectively. For certain sets in ${\rm {\bf R}}^d$ of integer Hausdorff dimension, we show that the limiting behavior of the best-packing distance as well as the minimal $s$-energy for large $s$ is different for different subsequences of the cardinalities of the configurations.

Given a compact $d$-rectifiable set $A$ embedded in Euclidean space and a distribution $\rho(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, we address the following question: how can one generate optimal configurations of $N$ points on $A$ that are "well-separated" and have asymptotic distribution $\rho (x)$ as $N\to \infty$? For this purpose we investigate minimal weighted Riesz energy points, that is, points interacting via the weighted power law potential $V=w(x,y)|x-y|^{-s}$, where $s>0$ is a fixed parameter and $w$ is suitably chosen. In the unweighted case ($w\equiv 1$) such points for $N$ fixed tend to the solution of the best-packing problem on $A$ as the parameter $s\to \infty$.

We present distance measurements to 71 high redshift type la supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands, as part of the CFHT Legacy Survey (CFHTLS). Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multi-band photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: ΩM = 0.263 ± 0.042 (stat) ± 0.032 (sys) for a flat ACDM model; and w = -1.023 ± 0.090 (stat) ± 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations. © ESO 2006.

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z=1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multi-band photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results : Omega_M = 0.263 +/- 0.042(stat) +/- 0.032(sys) for a flat LambdaCDM model; and w = -1.023 +/- 0.090(stat) +/- 0.054(sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations., Comment: (The SNLS Collaboration) 24 pages, 13 figures, Accepted in A&A. Computer readable tables at http://snls.in2p3.fr/conf/papers/cosmo1/

We present optical spectra of the peculiar Type Ia supernova (SN Ia) 1999ac. The data extend from -15 to +42 days with respect to B-band maximum and reveal an event that is unusual in several respects. Prior to B-band maximum, the spectra resemble those of SN 1999aa, a slowly declining event, but possess stronger SiII and CaII signatures (more characteristic of a spectroscopically normal SN). Spectra after B-band maximum appear more normal. The expansion velocities inferred from the Iron lines appear to be lower than average; whereas, the expansion velocity inferred from Calcium H and K are higher than average. The expansion velocities inferred from SiII are among the slowest ever observed, though SN 1999ac is not particularly dim. The analysis of the parameters v_10, R(SiII), dv(SiII)/dt, and d_m15 further underlines the unique characteristics of SN 1999ac. We find convincing evidence of CII 6580 in the day -15 spectrum with ejection velocity v > 16,000 km/s, but this signature disappears by day -9. This rapid evolution at early times highlights the importance of extremely early-time spectroscopy., 40 pages, 24 figures, accepted for publication in The Astronomical Journal

We present an extensive new time-series of spectroscopic data of the peculiar SN 1999aa in NGC 2595. Our data set includes 25 optical spectra between -11 and +58 days with respect to B-band maximum light, providing an unusually complete time history. The early spectra resemble those of a SN 1991T-like object but with a relatively strong Ca H&K absorption feature. The first clear sign of Si II 6355, characteristic of Type Ia supernovae, is found at day -7 and its velocity remains constant up to at least the first month after B-band maximum light. The transition to normal-looking spectra is found to occur earlier than in SN 1991T suggesting SN 1999aa as a possible link between SN 1991T-like and Branch-normal supernovae. Comparing the observations with synthetic spectra, doubly ionized Fe, Si and Ni are identified at early epochs. These are characteristic of SN 1991T-like objects. Furthermore, in the day -11 spectrum, evidence is found for an absorption feature which could be identified as high velocity C II 6580 or H-alpha. At the same epoch C III 4648.8 at photospheric velocity is probably responsible for the absorption feature at 4500 A. High velocity Ca is found around maximum light together with Si II and Fe II confined in a narrow velocity window. Implied constraints on supernovae progenitor systems and explosion hydrodynamical models are briefly discussed., 46 pages including 23 figures. Accepted for publication by AJ. For full-resolution figures see http://www.physto.se/~gabri/sn99aa/