Superharmonic Perturbations of a Gaussian Measure, Equilibrium Measures and Orthogonal Polynomials

This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a compactly supported positive measure $\mu$. The equilibrium measure of the corresponding weighted energy problem is shown to be supported on subharmonic generalized quadrature domains for a large class of perturbing potentials $U^{\mu}(z)$. It is also shown that the $2\times 2$ matrix d-bar problem for orthogonal polynomials with respect to such weights is well-defined and has a unique solution given explicitly by Cauchy transforms. Numerical evidence is presented supporting a conjectured relation between the asymptotic distribution of the zeroes of the orthogonal polynomials in a semi-classical scaling limit and the Schwarz function of the curve bounding the support of the equilibrium measure, extending the previously studied case of harmonic polynomial perturbations with weights $w(z)$ supported on a compact domain.Comment: CRM preprint, 28 pages. To appear in: Complex Analysis and Operator Theory (Special volume in honour of Bjorn Gustafsson). Two references added (Oct. 2, 2008

Spread of \u3ci\u3eAcentria Ephemerella\u3c/i\u3e (Lepidoptera: Pyralidae) in Central North America

The aquatic moth, Acentria ephemerella, was first reported from North America in 1927. Recent records from widespread localities in central North America indicate that the range of this European introduction continues to expand. The moth is well established in the western Great Lakes region and is recorded west to the Missouri River valley in Iowa

Host Range Extension for \u3ci\u3eChlorochlamys Chloroleucaria\u3c/i\u3e (Geometrinae, Geometridae) to Include \u3ci\u3eEriogonum Alatum\u3c/i\u3e (Polygonaceae)

(excerpt) Chlorochlamys chloroleucaria (Guenée) is a common moth of eastern North America, recorded from Nova Scotia south to Cuba and Mexico and as far west as Manitoba, the Black Hills of South Dakota, Wyoming and central Colorado (Boulder and El Paso counties) (Ferguson 1985)

Magnetic and Transport Properties of Fe-Ag granular multilayers

Results of magnetization, magnetotransport and Mossbauer spectroscopy measurements of sequentially evaporated Fe-Ag granular composites are presented. The strong magnetic scattering of the conduction electrons is reflected in the sublinear temperature dependence of the resistance and in the large negative magnetoresistance. The simultaneous analysis of the magnetic properties and the transport behavior suggests a bimodal grain size distribution. A detailed quantitative description of the unusual features observed in the transport properties is given

Line Emission in the Brightest Cluster Galaxies of the NOAO Fundamental Plane and Sloan Digital Sky Surveys

We examine the optical emission line properties of Brightest Cluster Galaxies (BCGs) selected from two large, homogeneous datasets. The first is the X-ray selected National Optical Astronomy Observatory Fundamental Plane Survey (NFPS), and the second is the C4 catalogue of optically selected clusters built from the Sloan Digital Sky Survey Data Release ~3 (SDSS DR3). Our goal is to better understand the optical line emission in BCGs with respect to properties of the galaxy and the host cluster. Throughout the analysis we compare the line emission of the BCGs to that of a control sample made of the other bright galaxies near the cluster centre. Overall, both the NFPS and SDSS show a modest fraction of BCGs with emission lines (~15%). No trend in the fraction of emitting BCGs as a function of galaxy mass or cluster velocity dispersion is found. However we find that, for those BCGs found in cooling flow clusters, 71^{+9}_{-14}% have optical emission. Furthermore, if we consider only BCGs within 50kpc of the X-ray centre of a cooling flow cluster, the emission-line fraction rises further to 100^{+0}_{-15}%. Excluding the cooling flow clusters, only ~10% of BCGs are line emitting, comparable to the control sample of galaxies. We show that the physical origin of the emission line activity varies: in some cases it has LINER-like line ratios, whereas in others it is a composite of star-formation and LINER-like activity. We conclude that the presence of emission lines in BCGs is directly related to the cooling of X-ray gas at the cluster centre.Comment: Accepted for publication in MNRAS. 13 pages mn2e style with 7 figures and 2 table

The Routing of Complex Contagion in Kleinberg's Small-World Networks

In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after $k \ge 2$ neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where we can activate one node at one time step with the goal of activating the targeted node in the end. We consider decentralized routing scheme where only the weak ties from the activated nodes are revealed. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all nodes that could be activated are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in $n$ (the number of nodes in the network) for all range of $\alpha$ both in expectation and with high probability (in particular, $\Omega(n^{\frac{1}{\alpha+2}})$ for $\alpha \le 2$ and $\Omega(n^{\frac{\alpha}{2(\alpha+2)}})$ for $\alpha > 2$ in expectation), while the routing time of simple contagion has polylogarithmic upper bound when $\alpha = 2$. Our results indicate that complex routing is harder than complex diffusion and the routing time of complex contagion differs exponentially compared to simple contagion at sweetspot.Comment: Conference version will appear in COCOON 201

The Evolution of [OII] Emission from Cluster Galaxies

We investigate the evolution of the star formation rate in cluster galaxies. We complement data from the CNOC1 cluster survey (0.15<z<0.6) with measurements from galaxy clusters in the 2dF galaxy redshift survey (0.05<z<0.1) and measurements from recently published work on higher redshift clusters, up to almost z=1. We focus our attention on galaxies in the cluster core, ie. galaxies with r<0.7h^{-1}_{70}Mpc. Averaging over clusters in redshift bins, we find that the fraction of galaxies with strong [OII] emission is < 20% in cluster cores, and the fraction evolves little with redshift. In contrast, field galaxies from the survey show a very strong increase over the same redshift range. It thus appears that the environment in the cores of rich clusters is hostile to star formation at all the redshifts studied. We compare this result with the evolution of the colours of galaxies in cluster cores, first reported by Butcher & Oemler (1984). Using the same galaxies for our analysis of the [OII] emission, we confirm that the fraction of blue galaxies, which are defined as galaxies 0.2 mag bluer in the rest frame B-V than the red sequence of each cluster, increases strongly with redshift. Since the colours of galaxies retain a memory of their recent star formation history, while emission from the [OII] line does not, we suggest that these two results can best be reconciled if the rate at which the clusters are being assembled is higher in the past, and the galaxies from which it is being assembled are typically bluer.Comment: 8 pages, 7 figures, accepted for publication in MNRA