Local Guarantees in Graph Cuts and Clustering

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$ or $-$ and the goal is to produce a clustering that agrees with the labels as much as possible: $+$ edges within clusters and $-$ edges across clusters. The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize a global objective. We depart from this and study local objectives: minimizing the maximum number of disagreements for edges incident on a single node, and the analogous max min agreements objective. This naturally gives rise to a family of basic min-max graph cut problems. A prototypical representative is Min Max $s-t$ Cut: find an $s-t$ cut minimizing the largest number of cut edges incident on any node. We present the following results: $(1)$ an $O(\sqrt{n})$-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node (thus providing the first known approximation for the above family of min-max graph cut problems), $(2)$ a remarkably simple $7$-approximation for minimizing local disagreements in complete graphs (improving upon the previous best known approximation of $48$), and $(3)$ a $1/(2+\varepsilon)$-approximation for maximizing the minimum total weight of agreement edges incident on any node, hence improving upon the $1/(4+\varepsilon)$-approximation that follows from the study of approximate pure Nash equilibria in cut and party affiliation games

The use and calibration of read-out streaks to increase the dynamic range of the Swift Ultraviolet/Optical Telescope

The dynamic range of photon counting micro-channel-plate (MCP) intensified charged-coupled device (CCD) instruments such as the Swift Ultraviolet/Optical Telescope (UVOT) and the XMM-Newton Optical Monitor (XMM-OM) is limited at the bright end by coincidence loss, the superposition of multiple photons in the individual frames recorded by the CCD. Photons which arrive during the brief period in which the image frame is transferred for read out of the CCD are displaced in the transfer direction in the recorded images. For sufficiently bright sources, these displaced counts form read-out streaks. Using UVOT observations of Tycho-2 stars, we investigate the use of these read-out streaks to obtain photometry for sources which are too bright (and hence have too much coincidence loss) for normal aperture photometry to be reliable. For read-out-streak photometry, the bright-source limiting factor is coincidence loss within the MCPs rather than the CCD. We find that photometric measurements can be obtained for stars up to 2.4 magnitudes brighter than the usual full-frame coincidence-loss limit by using the read-out streaks. The resulting bright-limit Vega magnitudes in the UVOT passbands are UVW2=8.80, UVM2=8.27, UVW1=8.86, u=9.76, b=10.53, v=9.31 and White=11.71; these limits are independent of the windowing mode of the camera. We find that a photometric precision of 0.1 mag can be achieved through read-out streak measurements. A suitable method for the measurement of read-out streaks is described and all necessary calibration factors are given.Comment: 11 pages, accepted for publication in MNRAS. Code available from the calibration link at http://www.mssl.ucl.ac.uk/www_astro/uvo

The incidence of obscuration in active galactic nuclei

We study the incidence of nuclear obscuration on a complete sample of 1310 AGN selected on the basis of their rest-frame 2-10 keV X-ray flux from the XMM-COSMOS survey, in the redshift range 0.3<z<3.5. We classify the AGN as obscured or un-obscured on the basis of either the optical spectral properties and the overall SED or the shape of the X-ray spectrum. The two classifications agree in about 70% of the objects, and the remaining 30% can be further subdivided into two distinct classes: at low luminosities X-ray un-obscured AGN do not always show signs of broad lines or blue/UV continuum emission in their optical spectra, most likely due to galaxy dilution effects; at high luminosities broad line AGN may have absorbed X-ray spectra, which hints at an increased incidence of small-scale (sub-parsec) dust-free obscuration. We confirm that the fraction of obscured AGN is a decreasing function of the intrinsic X-ray luminosity, while the incidence of absorption shows significant evolution only for the most luminous AGN, which appear to be more commonly obscured at higher redshift. We find no significant difference between the mean stellar masses and star formation rates of obscured and un-obscured AGN hosts. We conclude that the physical state of the medium responsible for obscuration in AGN is complex, and mainly determined by the radiation environment (nuclear luminosity) in a small region enclosed within the gravitational sphere of influence of the central black hole, but is largely insensitive to the wider scale galactic conditions.Comment: 18 pages, 17 figures, 2 tables. Accepted for publication by MNRA

The FMOS-COSMOS survey of star-forming galaxies at z ~ 1.6. I. H\alpha -based star formation rates and dust extinction

We present the first results from a near-IR spectroscopic survey of the COSMOS field, using the Fiber Multi-Object Spectrograph on the Subaru telescope, designed to characterize the star-forming galaxy population at $1.4<z<1.7$. The high-resolution mode is implemented to detect H$\alpha$ in emission between $1.6{\rm -}1.8 \mathrm{\mu m}$ with $f_{\rm H\alpha}\gtrsim4\times10^{-17}$ erg cm$^{-2}$ s$^{-1}$. Here, we specifically focus on 271 sBzK-selected galaxies that yield a H$\alpha$ detection thus providing a redshift and emission line luminosity to establish the relation between star formation rate and stellar mass. With further $J$-band spectroscopy for 89 of these, the level of dust extinction is assessed by measuring the Balmer decrement using co-added spectra. We find that the extinction ($0.6\lesssim A_\mathrm{H\alpha} \lesssim 2.5$) rises with stellar mass and is elevated at high masses compared to low-redshift galaxies. Using this subset of the spectroscopic sample, we further find that the differential extinction between stellar and nebular emission \hbox{$E_\mathrm{star}(B-V)/E_\mathrm{neb}(B-V)$} is 0.7--0.8, dissimilar to that typically seen at low redshift. After correcting for extinction, we derive an H$\alpha$-based main sequence with a slope ($0.81\pm0.04$) and normalization similar to previous studies at these redshifts.Comment: 6 pages, 4 figures, and 1 table. Published in ApJ Letter

The central energy source of 70micron-selected galaxies: Starburst or AGN?

We present the first AGN census in a sample of 61 galaxies selected at 70microns, a wavelength which should strongly favour the detection of star-forming systems. For the purpose of this study we take advantage of deep Chandra X-ray and Spitzer infrared (3.6-160micron) data, as well as optical spectroscopy and photometry from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey for the Extended Groth Strip (EGS) field. We investigate spectral line diagnostics ([OIII]/Hbeta and [NeIII]/[OII] ratios, Hdelta Balmer absorption line equivalent widths and the strength of the 4000Ang break), X-ray luminosities and spectral energy distributions (SEDs). We find that the 70micron sources are undergoing starburst episodes and are therefore characterised by a predominance of young stars. In addition, 13 per cent of the sources show AGN signatures and hence potentially host an AGN. When the sample is split into starbursts (SBs, 10^10<L_IR<10^11 L_solar), Luminous InfraRed Galaxies (LIRGs, 10^11<L_IR<10^12 L_solar) and UltraLuminous InfraRed Galaxies (ULIRGs,10^12<L_IR<10^13 L_solar), the AGN fraction becomes 0, 11 and 23 per cent respectively, showing an increase with total infrared luminosity. However, by examining the sources' panchromatic SEDs, we conclude that although the AGN is energetically important in 1 out of 61 objects, all 70micron-selected galaxies are primarily powered by star-formation.Comment: 20 pages, 14 figures, accepted for publication in MNRA

The ultraviolet luminosity function of star-forming galaxies between redshifts of 0.6 and 1.2

We use ultraviolet imaging taken with the XMM-Newton Optical Monitor telescope (XMM-OM), covering 280 square arcminutes in the UVW1 band (effective wavelength 2910 Angstroms) to measure rest-frame ultraviolet (1500 Angstrom) luminosity functions of galaxies with redshifts z between 0.6 and 1.2. The XMM-OM data are supplemented by a large body of optical and infrared imaging to provide photometric redshifts. The XMM-OM data have a significantly narrower point-spread-function (resulting in less source confusion) and simpler K-correction than the GALEX data previously employed in this redshift range. Ultraviolet-bright active galactic nuclei are excluded to ensure that the luminosity functions relate directly to the star-forming galaxy population. Binned luminosity functions and parametric Schechter-function fits are derived in two redshift intervals: 0.6<z<0.8 and 0.8<z<1.2. We find that the luminosity function evolves such that the characteristic absolute magnitude M* is brighter for 0.8<z<1.2 than for 0.6<z<0.8.Comment: 17 pages, 11 figures, accepted for publication in MNRA

A Population of Dust-rich Quasars at z ~ 1.5

We report Herschel SPIRE (250, 350, and 500 μm) detections of 32 quasars with redshifts 0.5 ≤z < 3.6 from the Herschel Multi-tiered Extragalactic Survey (HerMES). These sources are from a MIPS 24 μm flux-limited sample of 326 quasars in the Lockman Hole Field. The extensive multi-wavelength data available in the field permit construction of the rest-frame spectral energy distributions (SEDs) from ultraviolet to the mid-infrared for all sources, and to the far-infrared (FIR) for the 32 objects. Most quasars with Herschel FIR detections show dust temperatures in the range of 25-60 K, with a mean of 34 K. The FIR luminosities range from 10^(11.3) to 10^(13.5) L_☉, qualifying most of their hosts as ultra- or hyper-luminous infrared galaxies. These FIR-detected quasars may represent a dust-rich population, but with lower redshifts and fainter luminosities than quasars observed at ~1 mm. However, their FIR properties cannot be predicted from shorter wavelengths (0.3-20 μm, rest frame), and the bolometric luminosities derived using the 5100 Å index may be underestimated for these FIR-detected quasars. Regardless of redshift, we observed a decline in the relative strength of FIR luminosities for quasars with higher near-infrared luminosities

The evolution of the dust temperatures of galaxies in the SFR–M∗plane up to z ~ 2

We study the evolution of the dust temperature of galaxies in the SFR−M ∗ plane up to z ∼ 2 using far-infrared and submillimetre observations from the Herschel Space Observatory taken as part of the PACS Evolutionary Probe (PEP) and Herschel Multi-tiered Extragalactic Survey (HerMES) guaranteed time key programmes. Starting from a sample of galaxies with reliable star-formation rates (SFRs), stellar masses (M ∗ ) and redshift estimates, we grid the SFR−M ∗ parameter space in several redshift ranges and estimate the mean dust temperature (T dust ) of each SFR–M ∗ −z bin. Dust temperatures are inferred using the stacked far-infrared flux densities (100–500μm) of our SFR–M ∗ −z bins. At all redshifts, the dust temperature of galaxies smoothly increases with rest-frame infrared luminosities (L IR ), specific SFRs (SSFR; i.e., SFR/M ∗ ), and distances with respect to the main sequence (MS) of the SFR−M ∗ plane (i.e., Δlog(SSFR) MS = log[SSFR(galaxy)/SSFR MS (M ∗ ,z)]). The T dust −SSFR and T dust – Δlog(SSFR) MS correlations are statistically much more significant than the T dust −L IR one. While the slopes of these three correlations are redshift-independent, their normalisations evolve smoothly from z = 0 and z ∼ 2. We convert these results into a recipe to derive T dust from SFR, M ∗ and z, valid out to z ∼ 2 and for the stellar mass and SFR range covered by our stacking analysis. The existence of a strong T dust −Δlog(SSFR) MS correlation provides us with several pieces of information on the dust and gas content of galaxies. Firstly, the slope of the T dust −Δlog(SSFR) MS correlation can be explained by the increase in the star-formation efficiency (SFE; SFR/M gas ) with Δlog(SSFR) MS as found locally by molecular gas studies. Secondly, at fixed Δlog(SSFR) MS , the constant dust temperature observed in galaxies probing wide ranges in SFR and M ∗ can be explained by an increase or decrease in the number of star-forming regions with comparable SFE enclosed in them. And thirdly, at high redshift, the normalisation towards hotter dust temperature of the T dust −Δlog(SSFR) MS correlation can be explained by the decrease in the metallicities of galaxies or by the increase in the SFE of MS galaxies. All these results support the hypothesis that the conditions prevailing in the star-forming regions of MS and far-above-MS galaxies are different. MS galaxies have star-forming regions with low SFEs and thus cold dust, while galaxies situated far above the MS seem to be in a starbursting phase characterised by star-forming regions with high SFEs and thus hot dust