Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

Star formation histories and evolution of 35 brightest E+A galaxies from SDSS DR5

We pick out the 35 brightest galaxies from Goto's E+A galaxies catalogue which are selected from the Sloan Digital Sky Survey Data Release 5. The spectra of E+As are prominently characterized by the strong Balmer absorption lines but little [Oii] or H_alpha emission lines. In this work we study the stellar populations of the sample galaxies by fitting their spectra using ULySS, which is a robust full spectrum fitting method. We fit each of the sample with 1-population (a single stellar population-a SSP) and 3-population (3 SSPs) models, separately. By 1-population fits, we obtain SSP-equivalent ages and metallicities which correspond to the `luminosity-weighted' averages. By 3-population fits, we divide components into three groups in age (old stellar population-OSP, intermediate-age stellar population-ISP, and young stellar population-YSP), and then get the optimal age, metallicity and population fractions in both mass and light for OSP, ISP and YSP. During the fits, both Pegase.HR/Elodie3.1 and Vazdekis/Miles are used as two independent population models. The two models result in generally consistent conclusions as follows: for all the sample galaxies, YSPs (< 1Gyr) make important contributions to the light. However, the dominant contributors to mass are OSPs. We also reconstruct the smoothing star formation histories (SFHs) by giving star formation rate (SFR) versus evolutionary age. In addition, we fit the E+A sample and 34 randomly selected elliptical galaxies with 2-population (2 SSPs) model. We obtain the equivalent age of old components for each of the E+A sample and elliptical galaxies. By comparison, the old components of E+As are statistically much younger than those of ellipticals. From the standpoint of the stellar population age, this probably provides an evidence for the proposed evolutionary link from E+As to early-types (E/S0s).Comment: 16 pages, 9 figures, Accepted for publication on MNRA

Determining the Cosmic Distance Scale from Interferometric Measurements of the Sunyaev-Zel'dovich Effect

We determine the distances to 18 galaxy clusters with redshifts ranging from z~0.14 to z~0.78 from a maximum likelihood joint analysis of 30 GHz interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. These distances imply a Hubble constant of 60 (+4, -4) (+13, -18) km s-1 Mpc-1 for an Omega_M = 0.3, Omega_Lambda = 0.7 cosmology, where the uncertainties correspond to statistical followed by systematic at 68% confidence. With a sample of 18 clusters, systematic uncertainties clearly dominate. The systematics are observationally approachable and will be addressed in the coming years through the current generation of X-ray satellites (Chandra & XMM-Newton) and radio observatories (OVRO, BIMA, & VLA). Analysis of high redshift clusters detected in future SZE and X-ray surveys will allow a determination of the geometry of the universe from SZE determined distances.Comment: ApJ Submitted; 40 pages, 9 figures (fig 3 B&W for size constraint), 13 tables, uses emulateapj5 styl

Substructure lensing in galaxy clusters as a constraint on low-mass sterile neutrinos in tensor-vector-scalar theory: The straight arc of Abell 2390

Certain covariant theories of the modified Newtonian dynamics paradigm seem to require an additional hot dark matter (HDM) component - in the form of either heavy ordinary neutrinos or more recently light sterile neutrinos (SNs) with a mass around 11eV - to be relieved of problems ranging from cosmological scales down to intermediate ones relevant for galaxy clusters. Here we suggest using gravitational lensing by galaxy clusters to test such a marriage of neutrino HDM and modified gravity, adopting the framework of tensor-vector-scalar theory (TeVeS). Unlike conventional cold dark matter (CDM), such HDM is subject to strong phase-space constraints, which allows one to check cluster lens models inferred within the modified framework for consistency. Since the considered HDM particles cannot collapse into arbitrarily dense clumps and only form structures well above the galactic scale, systems which indicate the need for dark substructure are of particular interest. As a first example, we study the cluster lens Abell 2390 and its impressive straight arc with the help of numerical simulations. Based on our results, we outline a general and systematic approach to model cluster lenses in TeVeS which significantly reduces the calculation complexity. We further consider a simple bimodal lens configuration, capable of producing the straight arc, to demonstrate our approach. We find that such a model is marginally consistent with the hypothesis of 11eV SNs. Future work including more detailed and realistic lens models may further constrain the necessary SN distribution and help to conclusively assess this point. Cluster lenses could therefore provide an interesting discriminator between CDM and such modified gravity scenarios supplemented by SNs or other choices of HDM.Comment: 22 pages, 14 figures, 2 tables; minor changes to match accepted versio

Extreme emission-line galaxies out to z∼\sim1 in zCOSMOS. I. Sample and characterization of global properties

We present a thorough characterization of a large sample of 183 extreme emission-line galaxies (EELGs) at redshift 0.11 < z < 0.93 selected from the 20k zCOSMOS Bright Survey because of their unusually large emission line equivalent widths. We use multiwavelength COSMOS photometry, HST-ACS I-band imaging and optical zCOSMOS spectroscopy to derive the main global properties of EELGs, such as sizes, masses, SFRs, reliable metallicities from both "direct" and "strong-line" methods. The EELGs are compact (R_50 ~ 1.3 kpc), low-mass (log(M*/Msol)~7-10) galaxies forming stars at unusually high specific SFR (log(sSFR/yr) up to ~ -7) compared to main sequence SFGs of the same stellar mass and redshift. At UV wavelengths, the EELGs are luminous and show high surface brightness and include strong Ly$\alpha$ emitters, as revealed by GALEX spectroscopy. We show that zCOSMOS EELGs are high-ionization, low-metallicity systems, with median 12+log(O/H)=8.16, including a handful of extremely metal-deficient galaxies (<10% solar). While ~80% of the EELGs show non-axisymmetric morphologies, including clumpy and tadpole galaxies, we find that ~29% of them show additional low surface-brightness features, which strongly suggest recent or ongoing interactions. As star-forming dwarfs in the local Universe, EELGs are most often found in relative isolation. While only very few EELGs belong to compact groups, almost one third of them are found in spectroscopically confirmed loose pairs or triplets. We conclude that EELGs are galaxies caught in a transient and probably early period of their evolution, where they are efficiently building-up a significant fraction of their present-day stellar mass in an ongoing galaxy-wide starburst. Therefore, the EELGs constitute an ideal benchmark for comparison studies between low- and high-redshift low-mass star-forming galaxies.Comment: Accepted in A&A. Final replacement to match the version in press. It includes a minor change in the title and a new figur

The dependence of Galactic outflows on the properties and orientation of zCOSMOS galaxies at z ~ 1

We present an analysis of cool outflowing gas around galaxies, traced by MgII absorption lines in the co-added spectra of a sample of 486 zCOSMOS galaxies at 1 < z < 1.5. These galaxies span a range of stellar masses (9.45< log[M*/Msun]<10.7) and star formation rates (0.14 < log [SFR/Msun/yr] < 2.35). We identify the cool outflowing component in the MgII absorption and find that the equivalent width of the outflowing component increases with stellar mass. The outflow equivalent width also increases steadily with the increasing star formation rate of the galaxies. At similar stellar masses the blue galaxies exhibit a significantly higher outflow equivalent width as compared to red galaxies. The outflow equivalent width shows strong effect with star formation surface density ({\Sigma}SFR) of the sample. For the disk galaxies, the outflow equivalent width is higher for the face-on systems as compared to the edge-on ones, indicating that for the disk galaxies, the outflowing gas is primarily bipolar in geometry. Galaxies typically exhibit outflow velocities ranging from -200 km/s to -300 km/s and on average the face-on galaxies exhibit higher outflow velocity as compared to the edge-on ones. Galaxies with irregular morphologies exhibit outflow equivalent width as well as outflow velocities comparable to face on disk galaxies. These galaxies exhibit minimum mass outflow rates > 5-7 Msun/yr and a mass loading factor ({\eta} = dMout/dt /SFR) comparable to the star formation rates of the galaxies.Comment: 12 pages, 14 figures, ApJ submitte

zCOSMOS 20k: Satellite galaxies are the main drivers of environmental effects in the galaxy population at least to z~0.7

We explore the role of environment in the evolution of galaxies over 0.1<z<0.7 using the final zCOSMOS-bright data set. Using the red fraction of galaxies as a proxy for the quenched population, we find that the fraction of red galaxies increases with the environmental overdensity and with the stellar mass, consistent with previous works. As at lower redshift, the red fraction appears to be separable in mass and environment, suggesting the action of two processes: mass and environmental quenching. The parameters describing these appear to be essentially the same at z~0.7 as locally. We explore the relation between red fraction, mass and environment also for the central and satellite galaxies separately, paying close attention to the effects of impurities in the central-satellite classification and using carefully constructed samples matched in stellar mass. There is little evidence for a dependence of the red fraction of centrals on overdensity. Satellites are consistently redder at all overdensities, and the satellite quenching efficiency increases with overdensity at 0.1<z<0.4. This is less marked at higher redshift, but both are nevertheless consistent with the equivalent local measurements. At a given stellar mass, the fraction of galaxies that are satellites also increases with the overdensity. At a given overdensity and mass, the obtained relation between the environmental quenching and the satellite fraction agrees well with the satellite quenching efficiency, demonstrating that the environmental quenching in the overall population is consistent with being entirely produced through the satellite quenching process at least up to z=0.7. However, despite the unprecedented size of our high redshift samples, the associated statistical uncertainties are still significant and our statements should be understood as approximations to physical reality, rather than physically exact formulae.Comment: 22 pages, 19 figures, submitted to MNRA

Obscured AGN at z~1 from the zCOSMOS-Bright Survey I. Selection and Optical Properties of a [Ne v]-selected sample

A sample of 94 narrow line AGN with 0.65<z<1.20 has been selected from the 20k-Bright zCOSMOS galaxy sample by detection of the high-ionization [NeV]3426 line. Taking advantage of the large amount of data available in the COSMOS field, the properties of the [NeV]-selected Type-2 AGN have been investigated, focusing on their host galaxies, X-ray emission, and optical line flux ratios. Finally, the diagnostic developed by Gilli et al. (2010), based on the X-ray to [NeV] luminosity ratio, has been exploited to search for the more heavily obscured AGN. We found that [Ne v]-selected narrow line AGN have Seyfert 2-like optical spectra, although with emission line ratios diluted by a star-forming component. The ACS morphologies and stellar component in the optical spectra indicate a preference for our Type-2 AGN to be hosted in early-spirals with stellar masses greater than 10^(9.5-10)Msun, on average higher than those of the galaxy parent sample. The fraction of galaxies hosting [NeV]-selected obscured AGN increases with the stellar mass, reaching a maximum of about 3% at 2x10^11 Msun. A comparison with other selection techniques at z~1 shows that the detection of the [Ne v] line is an effective method to select AGN in the optical band, in particular the most heavily obscured ones, but can not provide by itself a complete census of AGN2. Finally, the high fraction of [NeV]-selected Type-2 AGN not detected in medium-deep Chandra observations (67%) is suggestive of the inclusion of Compton-thick sources in our sample. The presence of a population of heavily obscured AGN is corroborated by the X-ray to [NeV] ratio; we estimated, by mean of X-ray stacking technique and simulations, that the Compton-thick fraction in our sample of Type-2 AGN is 43+-4%, in good agreement with standard assumptions by the XRB synthesis models.Comment: 14 pages, 12 figures, accepted for publication in A&

The zCOSMOS 20k Group Catalog

We present an optical group catalog between 0.1 < z < 1 based on 16,500 high-quality spectroscopic redshifts in the completed zCOSMOS-bright survey. The catalog published herein contains 1498 groups in total and 192 groups with more than five observed members. The catalog includes both group properties and the identification of the member galaxies. Based on mock catalogs, the completeness and purity of groups with three and more members should be both about 83% with respect to all groups that should have been detectable within the survey, and more than 75% of the groups should exhibit a one-to-one correspondence to the "real" groups. Particularly at high redshift, there are apparently more galaxies in groups in the COSMOS field than expected from mock catalogs. We detect clear evidence for the growth of cosmic structure over the last seven billion years in the sense that the fraction of galaxies that are found in groups (in volume-limited samples) increases significantly with cosmic time. In the second part of the paper, we develop a method for associating galaxies that only have photo-z to our spectroscopically identified groups. We show that this leads to improved definition of group centers, improved identification of the most massive galaxies in the groups, and improved identification of central and satellite galaxies, where we define the former to be galaxies at the minimum of the gravitational potential wells. Subsamples of centrals and satellites in the groups can be defined with purities up to 80%, while a straight binary classification of all group and non-group galaxies into centrals and satellites achieves purities of 85% and 75%, respectively, for the spectroscopic sample.Comment: 26 pages, 21 figures, published in ApJ (along with machine-readable tables