Cluster versus POTENT Density and Velocity Fields: Cluster Biasing and Omega

The density and velocity fields as extracted from the Abell/ACO clusters are compared to the corresponding fields recovered by the POTENT method from the Mark~III peculiar velocities of galaxies. In order to minimize non-linear effects and to deal with ill-sampled regions we smooth both fields using a Gaussian window with radii ranging between 12 - 20\hmpc. The density and velocity fields within 70\hmpc exhibit similarities, qualitatively consistent with gravitational instability theory and a linear biasing relation between clusters and mass. The random and systematic errors are evaluated with the help of mock catalogs. Quantitative comparisons within a volume containing $\sim\!12$ independent samples yield \betac\equiv\Omega^{0.6}/b_c=0.22\pm0.08, where $b_c$ is the cluster biasing parameter at 15\hmpc. If $b_c \sim 4.5$, as indicated by the cluster correlation function, our result is consistent with $\Omega \sim 1$.Comment: 18 pages, latex, 2 ps figures 6 gif figures. Accepted for pubblications in MNRA

Cluster versus POTENT density and velocity fields:cluster biasing and Omega

The density and velocity fields as extracted from the Abell/ACO clusters are compared with the corresponding fields recovered by the POTENT method from the Mark III peculiar velocities of galaxies. In order to minimize non-linear effects and to deal with ill-sampled regions, we smooth both fields using a Gaussian window with radii ranging between 12 and 20 h(-1) Mpc. The density and velocity fields within 70 h(-1) Mpc exhibit similarities, qualitatively consistent with gravitational instability theory and a linear biasing relation between clusters and mass. The random and systematic errors are evaluated with the help of mock catalogues. Quantitative comparisons within a volume containing similar to 12 independent samples yield beta(c)=Omega(0.6)/b(c)=0.22 +/- 0.08, where b(c) is the cluster biasing parameter at 15 h(-1) Mpc. If b(c)similar to 4.5, as indicated by the cluster correlation function, our result is consistent with Omega similar to 1

Packing cycles faster than Erdos-Posa

The Cycle Packing problem asks whether a given undirected graph $G=(V,E)$ contains $k$ vertex-disjoint cycles. Since the publication of the classic Erdös--Pósa theorem in 1965, this problem received significant attention in the fields of graph theory and algorithm design. In particular, this problem is one of the first problems studied in the framework of parameterized complexity. The nonuniform fixed-parameter tractability of Cycle Packing follows from the Robertson--Seymour theorem, a fact already observed by Fellows and Langston in the 1980s. In 1994, Bodlaender showed that Cycle Packing can be solved in time $2^{\mathcal{O}(k^2)}\cdot |V|$ using exponential space. In the case a solution exists, Bodlaender's algorithm also outputs a solution (in the same time). It has later become common knowledge that Cycle Packing admits a $2^{\mathcal{O}(k\log^2k)}\cdot |V|$-time (deterministic) algorithm using exponential space, which is a consequence of the Erdös--Pósa theorem. Nowadays, the design of this algorithm is given as an exercise in textbooks on parameterized complexity. Yet, no algorithm that runs in time $2^{o(k\log^2k)}\cdot |V|^{\mathcal{O}(1)}$, beating the bound $2^{\mathcal{O}(k\log^2k)}\cdot |V|^{\mathcal{O}(1)}$, has been found. In light of this, it seems natural to ask whetherthe $2^{\mathcal{O}(k\log^2k)}\cdot |V|^{\mathcal{O}(1)}$ bound is essentially optimal. In this paper, we answer this question negatively by developing a $2^{\mathcal{O}(\frac{k\log^2k}{\log\log k})}\cdot |V|$-time (deterministic) algorithm for Cycle Packing. In the case a solution exists, our algorithm also outputs a solution (in the same time). Moreover, apart from beating the bound $2^{\mathcal{O}(k\log^2k)}\cdot |V|^{\mathcal{O}(1)}$, our algorithm runs in time linear in $|V|$, and its space complexity is polynomial in the input size.publishedVersio

Multi-User OFDM Based on Braided Convolutional Codes

Braided convolutional codes (BCCs) form a class of iteratively decodable convolutional codes that are constructed from component convolutional codes. In braided code division multiple access (BCDMA), these very efficient error correcting codes are combined with a multiple access method and inherent interleaving for channel diversity exploitation into one single scheme. In this paper, we describe the BCDMA principle and present simulation results for a frequency selective Rayleigh fading channel. Results for bit interleaved coded modulation (BICM) based on turbo and LDPC codes are also given for comparison

Gravitational Collapse with a Cosmological Constant

We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.Comment: 7 pages, 10 figures; To appear in Phys. Rev.

Galaxy clustering in the NEWFIRM Medium Band Survey: the relationship between stellar mass and dark matter halo mass at 1 < z < 2

We present an analysis of the clustering of galaxies as a function of their stellar mass at 1 < z < 2 using data from the NEWFIRM Medium Band Survey (NMBS). The precise photometric redshifts and stellar masses that the NMBS produces allows us to define a series of mass limited samples of galaxies more massive than 0.7, 1 and 3x10^10 Msun in redshift intervals centered on z = 1.1, 1.5 and 1.9 respectively. In each redshift interval we show that there exists a strong dependence of clustering strength on the stellar mass limit of the sample, with more massive galaxies showing a higher clustering amplitude on all scales. We further interpret our clustering measurements in the LCDM cosmological context using the halo model of galaxy clustering. We show that the typical halo mass of central and satellite galaxies increases with stellar mass, whereas the satellite fraction decreases with stellar mass, qualitatively the same as is seen at z < 1. We see little evidence of any redshift dependence in the stellar mass-to-halo mass relationship over our narrow redshift range. However, when we compare with similar measurements at z~0, we see clear evidence for a change in this relation. If we assume a universal baryon fraction, the ratio of stellar mass to halo mass reveals the fraction of baryons that have been converted to stars. We see that the peak in this star formation efficiency for central galaxies shifts to higher halo masses at higher redshift, moving from ~7x10^11 Msun at z~0 to ~3x10^12 Msun at z~1.5, revealing evidence of `halo downsizing'. Finally we show that for highly biased galaxy populations at z > 1 there may be a discrepancy between the measured space density and clustering and that predicted by the halo model. This could imply that there is a problem with one or more ingredients of the halo model at these redshifts, for instance the halo bias relation or the halo profile.Comment: Accepted for publication in ApJ. Correction made to typo in halo masses in conclusion

On the Prospect of Using the Maximum Circular Velocity of Halos to Encapsulate Assembly Bias in the Galaxy–Halo Connection

We investigate a conceptual modification of the halo occupation distribution approach, using the halos’ present-day maximal circular velocity, Vmax, as an alternative to halo mass. In particular, using a semianalytic galaxy formation model applied to the Millennium WMAP7 simulation, we explore the extent that switching to Vmax as the primary halo property incorporates the effects of assembly bias into the formalism. We consider fixed number density galaxy samples ranked by stellar mass and examine the variations in the halo occupation functions with either halo concentration or formation time. We find that using Vmax results in a significant reduction in the occupancy variation of the central galaxies, particularly for concentration. The satellites’ occupancy variation on the other hand increases in all cases. We find effectively no change in the halo clustering dependence on concentration, for fixed bins of Vmax compared to fixed halo mass. Most crucially, we calculate the impact of assembly bias on galaxy clustering by comparing the amplitude of clustering to that of a shuffled galaxy sample, finding that the level of galaxy assembly bias remains largely unchanged. Our results suggest that while using Vmax as a proxy for halo mass diminishes some of the occupancy variations exhibited in the galaxy–halo relation, it is not able to encapsulate the effects of assembly bias potentially present in galaxy clustering. The use of other more complex halo properties, such as Vpeak, the peak value of Vmax over the assembly history, provides some improvement and warrants further investigation