Network data and measurement.

Abstract Data on social networks may be gathered for all ties linking elements of a closed population ("complete" network data) or for the sets of ties surrounding sampled individual units ("egocentric" network data). Network data have been obtained via surveys and questionnaires, archives, observation, diaries, electronic traces, and experiments. Most methodological research on data quality concerns surveys and questionnaires. The question of the accuracy with which informants can provide data on their network ties is nontrivial, but survey methods can make some claim to reliability. Unresolved issues include whether to measure perceived social ties or actual exchanges, how to treat temporal elements in the definition of relationships, and whether to seek accurate descriptions or reliable indicators. Continued research on data quality is needed; beyond improved samples and further investigation of the informant accuracy/reliability issue, this should cover common indices of network structure, address the consequences of sampling portions of a network, and examine the robustness of indicators of network structure and position to both random and nonrandom errors of measurement

A Note on the Regularity of Inviscid Shell Model of Turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve the energy, provided that the components of the solution satisfy $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the ``two-dimensional'' parameters regime

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

A Bright Submillimeter Source in the Bullet Cluster (1E0657--56) Field Detected with BLAST

We present the 250, 350, and 500 micron detection of bright submillimeter emission in the direction of the Bullet Cluster measured by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). The 500 micron centroid is coincident with an AzTEC 1.1 mm point-source detection at a position close to the peak lensing magnification produced by the cluster. However, the 250 micron and 350 micron centroids are elongated and shifted toward the south with a differential shift between bands that cannot be explained by pointing uncertainties. We therefore conclude that the BLAST detection is likely contaminated by emission from foreground galaxies associated with the Bullet Cluster. The submillimeter redshift estimate based on 250-1100 micron photometry at the position of the AzTEC source is z_phot = 2.9 (+0.6 -0.3), consistent with the infrared color redshift estimation of the most likely IRAC counterpart. These flux densities indicate an apparent far-infrared luminosity of L_FIR = 2E13 Lsun. When the amplification due to the gravitational lensing of the cluster is removed, the intrinsic far-infrared luminosity of the source is found to be L_FIR <= 10^12 Lsun, consistent with typical luminous infrared galaxies.Comment: Accepted for publication in the Astrophysical Journal. Maps are available at http://blastexperiment.info

BLAST Observations of the South Ecliptic Pole field: Number Counts and Source Catalogs

We present results from a survey carried out by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) on a 9 deg^2 field near the South Ecliptic Pole at 250, 350 and 500 {\mu}m. The median 1{\sigma} depths of the maps are 36.0, 26.4 and 18.4 mJy, respectively. We apply a statistical method to estimate submillimeter galaxy number counts and find that they are in agreement with other measurements made with the same instrument and with the more recent results from Herschel/SPIRE. Thanks to the large field observed, the new measurements give additional constraints on the bright end of the counts. We identify 132, 89 and 61 sources with S/N>4 at 250, 350, 500 {\mu}m, respectively and provide a multi-wavelength combined catalog of 232 sources with a significance >4{\sigma} in at least one BLAST band. The new BLAST maps and catalogs are available publicly at http://blastexperiment.info.Comment: 25 pages, 6 figures, 4 tables, Accepted by ApJS. Maps and catalogs available at http://blastexperiment.info

Over half of the far-infrared background light comes from galaxies at z >= 1.2

Submillimetre surveys during the past decade have discovered a population of luminous, high-redshift, dusty starburst galaxies. In the redshift range 1 <= z <= 4, these massive submillimetre galaxies go through a phase characterized by optically obscured star formation at rates several hundred times that in the local Universe. Half of the starlight from this highly energetic process is absorbed and thermally re-radiated by clouds of dust at temperatures near 30 K with spectral energy distributions peaking at 100 microns in the rest frame. At 1 <= z <= 4, the peak is redshifted to wavelengths between 200 and 500 microns. The cumulative effect of these galaxies is to yield extragalactic optical and far-infrared backgrounds with approximately equal energy densities. Since the initial detection of the far-infrared background (FIRB), higher-resolution experiments have sought to decompose this integrated radiation into the contributions from individual galaxies. Here we report the results of an extragalactic survey at 250, 350 and 500 microns. Combining our results at 500 microns with those at 24 microns, we determine that all of the FIRB comes from individual galaxies, with galaxies at z >= 1.2 accounting for 70 per cent of it. As expected, at the longest wavelengths the signal is dominated by ultraluminous galaxies at z > 1.Comment: Accepted to Nature. Maps available at http://blastexperiment.info

Submillimeter Number Counts From Statistical Analysis of BLAST Maps

We describe the application of a statistical method to estimate submillimeter galaxy number counts from confusion limited observations by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). Our method is based on a maximum likelihood fit to the pixel histogram, sometimes called 'P(D)', an approach which has been used before to probe faint counts, the difference being that here we advocate its use even for sources with relatively high signal-to-noise ratios. This method has an advantage over standard techniques of source extraction in providing an unbiased estimate of the counts from the bright end down to flux densities well below the confusion limit. We specifically analyse BLAST observations of a roughly 10 sq. deg. map centered on the Great Observatories Origins Deep Survey South (GOODS-S) field. We provide estimates of number counts at the three BLAST wavelengths, 250, 350, and 500 microns; instead of counting sources in flux bins we estimate the counts at several flux density nodes connected with power-laws. We observe a generally very steep slope for the counts of about -3.7 at 250 microns and -4.5 at 350 and 500 microns, over the range ~0.02-0.5 Jy, breaking to a shallower slope below about 0.015 Jy at all three wavelengths. We also describe how to estimate the uncertainties and correlations in this method so that the results can be used for model-fitting. This method should be well-suited for analysis of data from the Herschel satellite.Comment: Accepted for publication in the Astrophysical Journal; see associated data and other papers at http://blastexperiment.info

Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

A panchromatic study of BLAST counterparts: total star-formation rate, morphology, AGN fraction and stellar mass

We carry out a multi-wavelength study of individual galaxies detected by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) and identified at other wavelengths, using data spanning the radio to the ultraviolet (UV). We develop a Monte Carlo method to account for flux boosting, source blending, and correlations among bands, which we use to derive deboosted far-infrared (FIR) luminosities for our sample. We estimate total star-formation rates for BLAST counterparts with z < 0.9 by combining their FIR and UV luminosities. Star formation is heavily obscured at L_FIR > 10^11 L_sun, z > 0.5, but the contribution from unobscured starlight cannot be neglected at L_FIR < 10^11 L_sun, z < 0.25. We assess that about 20% of the galaxies in our sample show indication of a type-1 active galactic nucleus (AGN), but their submillimeter emission is mainly due to star formation in the host galaxy. We compute stellar masses for a subset of 92 BLAST counterparts; these are relatively massive objects, with a median mass of ~10^11 M_sun, which seem to link the 24um and SCUBA populations, in terms of both stellar mass and star-formation activity. The bulk of the BLAST counterparts at z<1 appear to be run-of-the-mill star-forming galaxies, typically spiral in shape, with intermediate stellar masses and practically constant specific star-formation rates. On the other hand, the high-z tail of the BLAST counterparts significantly overlaps with the SCUBA population, in terms of both star-formation rates and stellar masses, with observed trends of specific star-formation rate that support strong evolution and downsizing.Comment: Accepted for publication in the Astrophysical Journal. 44 pages, 11 figures. The SED template for the derivation of L_FIR has changed (added new figure) and the discussion on the stellar masses has been improved. The complete set of full-color postage-stamps can be found at http://blastexperiment.info/results_images/moncelsi

BLAST05: Power Spectra of Bright Galactic Cirrus at Submillimeter Wavelengths

We report multi-wavelength power spectra of diffuse Galactic dust emission from BLAST observations at 250, 350, and 500 microns in Galactic Plane fields in Cygnus X and Aquila. These submillimeter power spectra statistically quantify the self-similar structure observable over a broad range of scales and can be used to assess the cirrus noise which limits the detection of faint point sources. The advent of submillimeter surveys with the Herschel Space Observatory makes the wavelength dependence a matter of interest. We show that the observed relative amplitudes of the power spectra can be related through a spectral energy distribution (SED). Fitting a simple modified black body to this SED, we find the dust temperature in Cygnus X to be 19.9 +/- 1.3 K and in the Aquila region 16.9 +/- 0.7 K. Our empirical estimates provide important new insight into the substantial cirrus noise that will be encountered in forthcoming observations.Comment: Submitted to the Astrophysical Journal. Maps and other data are available at http://blastexperiment.info