Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets

An identifying code of a (di)graph $G$ is a dominating subset $C$ of the vertices of $G$ such that all distinct vertices of $G$ have distinct (in)neighbourhoods within $C$. In this paper, we classify all finite digraphs which only admit their whole vertex set in any identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well known theorem of A. Bondy on set systems we classify the extremal cases for this theorem

Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted Identifying Code, (Open) Open Locating-Dominating Set and Metric Dimension) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP-complete, even for interval graphs of diameter 2 and permutation graphs of diameter 2. While Identifying Code and (Open) Locating-Dominating Set are trivially fixed-parameter-tractable when parameterized by solution size, it is known that in the same setting Metric Dimension is W[2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is fixed-parameter-tractable

Sequential Metric Dimension

International audienceSeager introduced the following game in 2013. An invisible and immobile target is hidden at some vertex of a graph $G$. Every step, one vertex $v$ of $G$ can be probed which results in the knowledge of the distance between $v$ and the target. The objective of the game is to minimize the number of steps needed to locate the target, wherever it is. We address the generalization of this game where $k ≥ 1$ vertices can be probed at every step. Our game also generalizes the notion of the metric dimension of a graph. Precisely, given a graph $G$ and two integers $k, ≥ 1$, the Localization Problem asks whether there exists a strategy to locate a target hidden in $G$ in at most steps by probing at most $k$ vertices per step. We show this problem is NP-complete when $k$ (resp.,) is a fixed parameter. Our main results are for the class of trees where we prove this problem is NP-complete when $k$ and are part of the input but, despite this, we design a polynomial-time (+1)-approximation algorithm in trees which gives a solution using at most one more step than the optimal one. It follows that the Localization Problem is polynomial-time solvable in trees if $k$ is fixed

Cosmic Shear Statistics and Cosmology

We report a measurement of cosmic shear correlations using an effective area of 6.5 sq. deg. of the VIRMOS deep imaging survey in progress at the Canada-France-Hawaii Telescope. We measured various shear correlation functions, the aperture mass statistic and the top-hat smoothed variance of the shear with a detection significance exceeding 12 sigma for each of them. We present results on angular scales from 3 arc-seconds to half a degree. The consistency of different statistical measures is demonstrated and confirms the lensing origin of the signal through tests that rely on the scalar nature of the gravitational potential. For Cold Dark Matter models we find $\sigma_8 \Omega_0^{0.6}=0.43^{+0.04}_{-0.05}$ at the 95% confidence level. The measurement over almost three decades of scale allows to discuss the effect of the shape of the power spectrum on the cosmological parameter estimation. The degeneracy on sigma_8-Omega_0 can be broken if priors on the shape of the linear power spectrum (that can be parameterized by Gamma) are assumed. For instance, with Gamma=0.21 and at the 95% confidence level, we obtain 0.60.65 and Omega_0<0.4 for flat (Lambda-CDM) models. From the tangential/radial modes decomposition we can set an upper limit on the intrinsic shape alignment, which was recently suggested as a possible contribution to the lensing signal. Within the error bars, there is no detection of intrinsic shape alignment for scales larger than 1'.Comment: 13 pages, submitted to A&

AEGIS: The Diversity of Bright Near-IR Selected Distant Red Galaxies

We use deep and wide near infrared (NIR) imaging from the Palomar telescope combined with DEEP2 spectroscopy and Hubble Space Telescope (HST) and Chandra Space Telescope imaging to investigate the nature of galaxies that are red in NIR colors. We locate these `distant red galaxies' (DRGs) through the color cut (J-K)_{vega} > 2.3 over 0.7 deg^{2}, where we find 1010 DRG candidates down to K_s = 20.5. We combine 95 high quality spectroscopic redshifts with photometric redshifts from BRIJK photometry to determine the redshift and stellar mass distributions for these systems, and morphological/structural and X-ray properties for 107 DRGs in the Extended Groth Strip. We find that many bright (J-K)_{vega}>2.3 galaxies with K_s2 systems massive with M_*>10^{11} M_solar. HST imaging shows that the structural properties and morphologies of DRGs are also diverse, with the majority elliptical/compact (57%), and the remainder edge-on spirals (7%), and peculiar galaxies (29%). The DRGs at z < 1.4 with high quality spectroscopic redshifts are generally compact, with small half light radii, and span a range in rest-frame optical properties. The spectral energy distributions for these objects differ from higher redshift DRGs: they are bluer by one magnitude in observed (I-J) color. A pure IR color selection of high redshift populations is not sufficient to identify unique populations, and other colors, or spectroscopic redshifts are needed to produce homogeneous samples

The VIMOS VLT Deep Survey - First epoch VVDS-Deep survey: 11564 spectra with 17.5<=IAB<=24, and the redshift distribution over 0< z <=5

This paper presents the ``First Epoch'' sample from the VIMOS VLT Deep Survey (VVDS). The VVDS goals, observations, data reduction with VIPGI, and redshift measurement with KBRED are discussed. Data have been obtained with the VIsible Multi Object Spectrograph (VIMOS) on the ESO-VLT UT3, allowing to observe ~600 slits simultaneously at R~230. A total of 11564 objects have been observed in the VVDS-02h and VVDS-CDFS Deep fields over a total area of 0.61deg^2, selected solely on the basis of apparent magnitude 17.5 <=I_{AB} <=24. The VVDS covers the redshift range 0 < z <= 5. It is successfully going through the ``redshift desert'' 1.5<z<2.2, while the range 2.2<z<2.7 remains of difficult access because of the VVDS wavelength coverage.A total of 9677 galaxies have a redshift measurement, 836 are stars, 90 are AGNs, and a redshift could not be measured for 961 objects. There are 1065 galaxies with a measured redshift z>1.4. The survey reaches a redshift measurement completeness of 78% overall (93% including less reliable objects), with a spatial sampling of the population of galaxies of 25% and ~30% in the VVDS-02h and VVDS-CDFS. The redshift accuracy measured from repeated observations with VIMOS and comparison to other surveys is ~276km/s. From this sample we present for the first time the redshift distribution of a magnitude limited spectroscopic sample down to IAB=24. The redshift distribution has a median of z=0.62, z=0.65, z=0.70, and z=0.76, for magnitude limited samples with IAB<=22.5, 23, 23.5, and 24. A high redshift tail above redshift 2 and up to redshift 5 becomes readily apparent for IAB>23.5, probing the bright star forming population of galaxies. This sample provides an unprecedented dataset to study galaxy evolution over 90% of the life of the universeComment: 30 pages, accepted 22-Feb-05 in A&

The sizes, masses and specific star formation rates of massive galaxies at 1.3 &lt; z &lt; 1.5: strong evidence in favour of evolution via minor mergers

We report the results of a comprehensive study of the relationship between galaxy size, stellar mass and specific star-formation rate (sSFR) at redshifts 1.3= 6x10^10 Msun), spectroscopic sample from the UKIDSS Ultra-deep Survey (UDS), with accurate stellar-mass measurements derived from spectro photometric fitting, we find that at z~1.4 the location of massive galaxies on the size-mass plane is determined primarily by their sSFR. At this epoch we find that massive galaxies which are passive (sSFR <= 0.1 Gyr^-1) follow a tight size-mass relation, with half-light radii a factor f=2.4+/-0.2 smaller than their local counterparts. Moreover, amongst the passive sub-sample we find no evidence that the off-set from the local size-mass relation is a function of stellar population age. Based on a sub-sample with dynamical mass estimates we also derive an independent estimate of f=2.3+/-0.3 for the typical growth in half-light radius between z~1.4 and the present day. Focusing on the passive sub-sample, we conclude that to produce the necessary evolution predominantly via major mergers would require an unfeasible number of merger events and over populate the high-mass end of the local stellar mass function. In contrast, we find that a scenario in which mass accretion is dominated by minor mergers can produce the necessary evolution, whereby an increase in stellar mass by a factor of ~2, accompanied by an increase in size by a factor of ~3.5, is sufficient to reconcile the size-mass relation at z~1.4 with that observed locally. Finally, we note that a significant fraction (44+/-12%) of the passive galaxies in our sample have a disk-like morphology, providing additional evidence that separate physical processes are responsible for the quenching of star-formation and the morphological transformation of massive galaxies (abridged).Comment: 21 pages, 11 figures, accepted for publication in MNRAS. Replaced to match accepted versio

The VIMOS-VLT Deep Survey - The evolution of galaxy clustering per spectral type to z~1.5

We measure the evolution of clustering for galaxies with different spectral types from 6495 galaxies with 17.5<=I_AB<=24 and measured spectroscopic redshift in the first epoch VIMOS-VLT Deep Survey. We classify our sample into 4 classes, based on the fit of well-defined galaxy spectral energy distributions on observed multi-color data. We measure the projected function wp(rp) and estimate the best-fit parameters for a power-law real-space correlation function. We find the clustering of early-spectral-type galaxies to be markedly stronger than that of late-type galaxies at all redshifts up to z<=1.2. At z~0.8, early-type galaxies display a correlation length r_0=4.8+/-0.9h^{-1}Mpc, while late types have r_0=2.5+/-0.4h^{-1}Mpc. The clustering of these objects increases up to r_0=3.42+/-0.7h^{-1}Mpc for z~1.4. The relative bias between early- and late-type galaxies within our magnitude-limited survey remains approximately constant with b~1.7-1.8 from z~=0.2 up to z~=1, with indications for a decrease at z>1.2, due to the growth in clustering of the star-forming population. We find similar results when splitting the sample into `red' and `blue' galaxies using the observed color bi-modality. When compared to the expected linear growth of mass fluctuations, a natural interpretation of these observations is that: (a) the assembly of massive early type galaxies is already mostly complete in the densest dark matter halos at z~=1; (b) luminous late-type galaxies are located in higher-density, more clustered regions of the Universe at z~=1.5 than at present, indicating that star formation activity is progressively increasing, going back in time, in the higher-density peaks that today are mostly dominated by old galaxies.Comment: 12 pages, Accepted on 11-Feb-06 for publication in Astronomy and Astrophysic

The Vimos VLT Deep Survey: Compact structures in the CDFS

We have used the Vimos VLT Deep Survey in combination with other spectroscopic, photometric and X-ray surveys from literature to detect several galaxy structures in the Chandra Deep Field South (CDFS). Both a friend-of-friend based algorithm applied to the spectroscopic redshift catalog and an adaptative kernel galaxy density and colour maps correlated with photometric redshift estimates have been used. We mainly detect a chain-like structure at z=0.66 and two massive groups at z=0.735 and 1.098 showing signs of ongoing collapse. We also detect two galaxy walls at z=0.66 and at z=0.735 (extremely compact in redshift space). The first one contains the chain-like structure and the last one contains in its center one of the two massive groups. Finally, other galaxy structures that are probably loose low mass groups are detected. We compare the group galaxy population with simulations in order to assess the richness of these structures and we study their galaxy morphological contents. The higher redshift structures appear to probably have lower velocity dispersion than the nearby ones. The number of moderatly massive structures we detect is consistent with what is expected for an LCDM model, but a larger sample is required to put significant cosmological constraints.Comment: 15 pages, 17 figures, accepted in A&