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 Comoving Infrared Luminosity Density: Domination of Cold Galaxies across 0<z<1

In this paper we examine the contribution of galaxies with different infrared (IR) spectral energy distributions (SEDs) to the comoving infrared luminosity density, a proxy for the comoving star formation rate (SFR) density. We characterise galaxies as having either a cold or hot IR SED depending upon whether the rest-frame wavelength of their peak IR energy output is above or below 90um. Our work is based on a far-IR selected sample both in the local Universe and at high redshift, the former consisting of IRAS 60um-selected galaxies at z<0.07 and the latter of Spitzer 70um selected galaxies across 0.1<z<1. We find that the total IR luminosity densities for each redshift/luminosity bin agree well with results derived from other deep mid/far-IR surveys. At z<0.07 we observe the previously known results: that moderate luminosity galaxies (L_IR<10^11 Lsun) dominate the total luminosity density and that the fraction of cold galaxies decreases with increasing luminosity, becoming negligible at the highest luminosities. Conversely, above z=0.1 we find that luminous IR galaxies (L_IR>10^11 Lsun), the majority of which are cold, dominate the IR luminosity density. We therefore infer that cold galaxies dominate the IR luminosity density across the whole 0<z<1 range, hence appear to be the main driver behind the increase in SFR density up to z~1 whereas local luminous galaxies are not, on the whole, representative of the high redshift population.Comment: 5 pages, 3 figures, accepted for publication in MNRA

Selection of ULIRGs in Infrared and Submm Surveys

We examine the selection characteristics of infrared and sub-mm surveys with IRAS, Spitzer, BLAST, Herschel and SCUBA and identify the range of dust temperatures these surveys are sensitive to, for galaxies in the ULIRG luminosity range (12<log(LIR)<13), between z=0 and z=4. We find that the extent of the redshift range over which surveys are unbiased is a function of the wavelength of selection, flux density limit and ULIRG luminosity. Short wavelength (<200{\mu}m) surveys with IRAS, Spitzer/MIPS and Herschel/PACS are sensitive to all SED types in a large temperature interval (17-87K), over a substantial fraction of their accessible redshift range. On the other hand, long wavelength (>200{\mu}m) surveys with BLAST, Herschel/ SPIRE and SCUBA are significantly more sensitive to cold ULIRGs, disfavouring warmer SEDs even at low redshifts. We evaluate observations in the context of survey selection effects, finding that the lack of cold ULIRGs in the local (z<0.1) Universe is not a consequence of selection and that the range of ULIRG temperatures seen locally is only a subset of a much larger range which exists at high redshift. We demonstrate that the local luminosity-temperature (L-T) relation, which indicates that more luminous sources are also hotter, is not applicable in the distant Universe when extrapolated to the ULIRG regime, because the scatter in observed temperatures is too large. Finally, we show that the difference between the ULIRG temperature distributions locally and at high redshift is not the result of galaxies becoming colder due to an L-T relation which evolves as a function of redshift. Instead, they are consistent with a picture where the evolution of the infrared luminosity function is temperature dependent, i.e. cold galaxies evolve at a faster rate than their warm counterparts.Comment: 11 pages, 6 figures, accepted for publication in MNRA

AEGIS: Infrared Spectral Energy Distributions of MIPS 70micron selected sources

We present 0.5 -160 micron Spectral Energy Distributions (SEDs) of galaxies, detected at 70microns with the Multiband Imaging Photometer for Spitzer (MIPS), using broadband imaging data from Spitzer and ground-based telescopes. Spectroscopic redshifts, in the range 0.2<z<1.5, have been measured as part of the Deep Extragalactic Evolutionary Probe2 (DEEP2) project. Based on the SEDs we explore the nature and physical properties of the sources. Using the optical spectra we derive Hbeta and [OII]-based Star Formation Rates (SFR) which are 10-100 times lower than SFR estimates based on IR and radio. The median offset in SFR between optical and IR is reduced by a factor of ~3 when we apply a typical extinction corrections. We investigate mid-to-far infrared correlations for low redshift (>0.5) and high redshift (0.5<z<1.2) bins. Using this unique ``far-infrared'' selected sample we derive an empirical mid to far-infrared relationship that can be used to estimate the infrared energy budget of galaxies in the high-redshift universe. Our sample can be used as a template to translate far-infrared luminosities into bolometric luminosities for high redshift objects.Comment: 4 pages, 5 figures, accepted for publication in AEGIS ApJL Special Issu

The link between SCUBA and Spitzer: cold galaxies at z lt 1

We show that the far-IR properties of distant Luminous and UltraLuminous InfraRed Galaxies (LIRGs and ULIRGs, respectively) are on average divergent from analogous sources in the local Universe. Our analysis is based on Spitzer Multiband Imaging Photometer (MIPS) and Infrared Array Camera (IRAC) data of LIR > 1010 L⊙, 70 μm selected objects in the 0.1 1 SubMillimetre Galaxies (SMGs) discovered in blank-field submillimetre surveys. The Herschel Space Observatory is well placed to fully characterize the nature of these objects, as its coverage extends over a major part of the far-IR/sub-mm SED for a wide redshift range

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

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 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