Matching random colored points with rectangles

Let S ¿ [0, 1]2 be a set of n points, randomly and uniformly selected. Let R ¿ B be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random number M(n) of points of S that are covered by the rectangles of a maximum strong matching of S with axis-aligned rectangles. The matching consists of closed rectangles that cover exactly two points of S of the same color. A matching is strong if all its rectangles are pairwise disjoint. We prove that almost surely M(n) = 0.83 n for n large enough. Our approach is based on modeling a deterministic greedy matching algorithm, that runs over the random point set, as a Markov chain.Postprint (published version

Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energy analysis (SEA) towards non-diffusive wave fields. DEA takes into account the full directionality of the wave field and makes sub-structuring obsolete. It can thus be implemented on mesh grids commonly used, for example, in the finite element method (FEM). The resulting mesh based formulation of DEA can be implemented very efficiently using discrete flow mapping (DFM) as detailed in [1] and described here for applications in vibro-acoustics

Southern Massive Stars at High Angular Resolution: Observational Campaign and Companion Detection

Multiplicity is one of the most fundamental observable properties of massive O-type stars and offers a promising way to discriminate between massive star formation theories. Nevertheless, companions at separations between 1 and 100 mas remain mostly unknown due to intrinsic observational limitations. [...] The Southern MAssive Stars at High angular resolution survey (SMASH+) was designed to fill this gap by providing the first systematic interferometric survey of Galactic massive stars. We observed 117 O-type stars with VLTI/PIONIER and 162 O-type stars with NACO/SAM, respectively probing the separation ranges 1-45 and 30-250mas and brightness contrasts of Delta H < 4 and Delta H < 5. Taking advantage of NACO's field-of-view, we further uniformly searched for visual companions in an 8''-radius down to Delta H = 8. This paper describes the observations and data analysis, reports the discovery of almost 200 new companions in the separation range from 1mas to 8'' and presents the catalog of detections, including the first resolved measurements of over a dozen known long-period spectroscopic binaries. Excluding known runaway stars for which no companions are detected, 96 objects in our main sample (DEC < 0 deg; H<7.5) were observed both with PIONIER and NACO/SAM. The fraction of these stars with at least one resolved companion within 200mas is 0.53. Accounting for known but unresolved spectroscopic or eclipsing companions, the multiplicity fraction at separation < 8'' increases to f_m = 0.91 +/- 0.03. The fraction of luminosity class V stars that have a bound companion reaches 100% at 30mas while their average number of physically connected companions within 8'' is f_c = 2.2 +/- 0.3. This demonstrates that massive stars form nearly exclusively in multiple systems. Additionally, the nine non-thermal (NT) radio emitters observed by SMASH+ are all resolved [...]Comment: 57 pages, 20 figures, 7 tables; accepted for publication in ApJ

No Evidence for Evolution in the Far-Infrared-Radio Correlation out to z ~ 2 in the eCDFS

We investigate the 70 um Far-Infrared Radio Correlation (FRC) of star-forming galaxies in the Extended Chandra Deep Field South (ECDFS) out to z > 2. We use 70 um data from the Far-Infrared Deep Extragalactic Legacy Survey (FIDEL), which comprises the most sensitive (~0.8 mJy rms) and extensive far-infrared deep field observations using MIPS on the Spitzer Space Telescope, and 1.4 GHz radio data (~8 uJy/beam rms) from the VLA. In order to quantify the evolution of the FRC we use both survival analysis and stacking techniques which we find give similar results. We also calculate the FRC using total infrared luminosity and rest-frame radio luminosity, qTIR, and find that qTIR is constant (within 0.22) over the redshift range 0 - 2. We see no evidence for evolution in the FRC at 70 um which is surprising given the many factors that are expected to change this ratio at high redshifts.Comment: 18 pages, 13 figures. Accepted for publication in Ap

Ray and wave scattering in smoothly curved thin shell cylindrical ridges

We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model is analysed via an appropriate phase-plane analysis, from which the fixed points can be interpreted in terms of the reflection and transmission properties. The corresponding full wave scattering model is studied using the finite difference method to investigate the scattering properties of an incident plane wave. Through both models we uncover the scattering properties of smoothed joints in the interesting mid-frequency region close to the ring frequency, where there is a qualitative change in the dynamics from anisotropic to simple geodesic propagation

Multiwavelength characterization of faint ultra steep spectrum radio sources: a search for high-redshift radio galaxies

Context. Ultra steep spectrum (USS) radio sources are one of the efficient tracers of powerful high-z radio galaxies (HzRGs). In contrast to searches for powerful HzRGs from radio surveys of moderate depths, fainter USS samples derived from deeper radio surveys can be useful in finding HzRGs at even higher redshifts and in unveiling a population of obscured weaker radio-loud AGN at moderate redshifts. Aims. Using our 325 MHz GMRT observations (5σ ∼ 800 μJy) and 1.4 GHz VLA observations (5σ ∼ 80−100 μJy) available in two subfields (VLA-VIMOS VLT Deep Survey (VLA-VVDS) and Subaru X-ray Deep Field (SXDF)) of the XMM-LSS field, we derive a large sample of 160 faint USS radio sources and characterize their nature. Methods. The optical and IR counterparts of our USS sample sources are searched using existing deep surveys, at respective wavelengths. We attempt to unveil the nature of our faint USS sources using diagnostic techniques based on mid-IR colors, flux ratios of radio to mid-IR, and radio luminosities. Results. Redshift estimates are available for 86/116 (∼74%) USS sources in the VLA-VVDS field and for 39/44 (∼87%) USS sources in the SXDF fields with median values (zmedian) ∼1.18 and ∼1.57, respectively, which are higher than estimates for non-USS radio sources (zmedian non−USS ∼ 0.99 and ∼0.96), in the two subfields. The MIR color–color diagnostic and radio luminosities are consistent with most of our USS sample sources at higher redshifts (z > 0.5) being AGN. The flux ratio of radio to mid-IR (S 1.4 GHz/S 3.6 μm) versus redshift diagnostic plot suggests that more than half of our USS sample sources distributed over z ∼ 0.5 to 3.8 are likely to be hosted in obscured environments. A significant fraction (∼26% in the VLA-VVDS and ∼13% in the SXDF) of our USS sources without redshift estimates mostly remain unidentified in the existing optical, IR surveys, and exhibit high radio to mid-IR flux ratio limits similar to HzRGs, and so, can be considered as potential HzRG candidates. Conclusions. Our study shows that the criterion of ultra steep spectral index remains a reasonably efficient method to select high-z sources even at sub-mJy flux densities. In addition to powerful HzRG candidates, our faint USS sample also contains populations of weaker radio-loud AGNs potentially hosted in obscured environments

High-resolution VLA Imaging of SDSS Stripe 82 at 1.4 GHz

We present a high-resolution radio survey of the Sloan Digital Sky Survey (SDSS) Southern Equatorial Stripe, a.k.a. Stripe 82. This 1.4 GHz survey was conducted with the Very Large Array (VLA) primarily in the A-configuration, with supplemental B-configuration data to increase sensitivity to extended structure. The survey has an angular resolution of 1.8" and achieves a median rms noise of 52 microJy/bm over 92 deg^2. This is the deepest 1.4 GHz survey to achieve this large of an area, filling a gap in the phase space between small, deep and large, shallow surveys. It also serves as a pilot project for a larger high-resolution survey with the Expanded Very Large Array (EVLA). We discuss the technical design of the survey and details of the observations, and we outline our method for data reduction. We present a catalog of 17,969 isolated radio components, for an overall source density of ~195 sources/deg^2. The astrometric accuracy of the data is excellent, with an internal check utilizing multiply-observed sources yielding an rms scatter of 0.19" in both right ascension and declination. A comparison to the SDSS DR7 Quasar Catalog further confirms that the astrometry is well tied to the optical reference frame, with mean offsets of 0.02" +/- 0.01" in right ascension, and 0.01" +/- 0.02" in declination. A check of our photometry reveals a small, negative CLEAN-like bias on the level of 35 microJy. We report on the catalog completeness, finding that 97% of FIRST-detected quasars are recovered in the new Stripe 82 radio catalog, while faint, extended sources are more likely to be resolved out by the resolution bias. We conclude with a discussion of the optical counterparts to the catalog sources, including 76 newly-detected radio quasars. The full catalog as well as a search page and cutout server are available online at http://third.ucllnl.org/cgi-bin/stripe82cutout.Comment: 18 pages, 22, figures. Submitted to AJ, revised to address referee's comment