Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.Comment: AAS Latex file, 44 pages, accepted for publication in Ap

Ethnic group differences in overweight and obese children and young people in England: cross sectional survey

Aims: To determine the percentage of children and young adults who are obese or overweight within different ethnic and socioeconomic groups.Methods: Secondary analysis of data on 5689 children and young adults aged 2 - 20 years from the 1999 Health Survey for England.Results: Twenty three per cent of children (n = 1311) were overweight, of whom 6% ( n = 358) were obese. More girls than boys were overweight ( 24% v 22%). Afro-Caribbean girls were more likely to be overweight ( odds ratio 1.73, 95% CI 1.29 to 2.33), and Afro-Caribbean and Pakistani girls were more likely to be obese than girls in the general population ( odds ratios 2.74 ( 95% CI 1.74 to 4.31) and 1.71 ( 95% CI 1.06 to 2.76), respectively). Indian and Pakistani boys were more likely to be overweight ( odds ratios 1.55 ( 95% CI 1.12 to 2.17) and 1.36 ( 95% CI 1.01 to 1.83), respectively). There were no significant differences in the prevalence of obese and overweight children from different social classes.Conclusion: The percentage of children and young adults who are obese and overweight differs by ethnic group and sex, but not by social class. British Afro-Caribbean and Pakistani girls have an increased risk of being obese and Indian and Pakistani boys have an increased risk of being overweight than the general population. These individuals may be at greater combined cumulative risk of morbidity and mortality from cardiovascular disease and so may be a priority for initiatives to target groups of children at particular risk of obesity

Velocity bias in a LCDM model

We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.Comment: 13 pages, Latex, AASTeXv5 and natbi

Star Formation at the Twilight of the Dark Ages: Which Stars Reionized the Universe?

We calculate the global star formation rate density (SFRD) from z ~ 30-3 using a semi-analytic model incorporating the hierarchical assembly of dark matter halos, gas cooling via atomic hydrogen, star formation, supernova feedback, and suppression of gas collapse in small halos due to the presence of a photoionizing background. We compare the results with the predictions of simpler models based on the rate of dark matter halo growth and a fixed ratio of stellar-to-dark mass, and with observational constraints on the SFRD at 3 < z < 6. We also estimate the star formation rate due to very massive, metal-free Pop III stars using a simple model based on the halo formation rate, calibrated against detailed hydrodynamic simulations of Pop III star formation. We find that the total production rate of hydrogen-ionizing photons during the probable epoch of reionization (15 < z < 20) is approximately equally divided between Pop II and Pop III stars, and that if reionization is late (less than about 15, close to the lower limit of the range allowed by the WMAP results), then Pop II stars alone may be able to reionize the Universe.Comment: submitted to ApJ

Physical Bias of Galaxies From Large-Scale Hydrodynamic Simulations

We analyze a new large-scale ($100h^{-1}$Mpc) numerical hydrodynamic simulation of the popular $\Lambda$CDM cosmological model, including in our treatment dark matter, gas and star-formation, on the basis of standard physical processes. The method, applied with a numerical resolution of $<200h^{-1}$kpc (which is still quite coarse for following individual galaxies, especially in dense regions), attempts to estimate where and when galaxies form. We then compare the smoothed galaxy distribution with the smoothed mass distribution to determine the "bias" defined as $b\equiv (\delta M/M)_{gal}/(\delta M/M)_{total}$ on scales large compared with the code numerical resolution (on the basis of resolution tests given in the appendix of this paper). We find that (holding all variables constant except the quoted one) bias increases with decreasing scale, with increasing galactic age or metallicity and with increasing redshift of observations. At the $8h^{-1}$Mpc fiducial comoving scale bias (for bright regions) is 1.35 at $z=0$ reaching to 3.6 at $z=3$, both numbers being consistent with extant observations. We also find that $(10-20)h^{-1}$Mpc voids in the distribution of luminous objects are as observed (i.e., observed voids are not an argument against CDM-like models) and finally that the younger systems should show a colder Hubble flow than do the early type galaxies (a testable proposition). Surprisingly, little evolution is found in the amplitude of the smoothed galaxy-galaxy correlation function (as a function of {\it comoving} separation). Testing this prediction vs observations will allow a comparison between this work and that of Kauffmann et al which is based on a different physical modelingmethod.Comment: in press, ApJ, 26 latex pages plus 7 fig

Quasi-one and two-dimensional transitions of gases adsorbed on nanotube bundles

Grand canonical Monte Carlo simulations have been performed to determine the adsorption behavior of Ar and Kr atoms on the exterior surface of a rope (bundle) consisting of many carbon nanotubes. The computed adsorption isotherms reveal phase transitions associated with the successive creation of quasi-one dimensional lines of atoms near and parallel to the intersection of two adjacent nanotubes.Comment: 12 pages, 6 figures, submitted to J. Chem. Phy

Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.Comment: 6 pages, 3 figure

Comparing the Evolution of the Galaxy Disk Sizes with CDM Models: The Hubble Deep Field

The intrinsic sizes of the field galaxies with I<26 in the Hubble and ESO-NTT Deep Fields are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalogs and are compared with the CDM predictions. Extending to lower luminosities and to higher z our previous analysis performed on the NTT field alone, we find that the distribution of the galaxy disk sizes at different cosmic epochs is within the range predicted by typical CDM models. However, the observed size distribution of faint (M_B>-19) galaxies is skewed with respect to the CDM predictions and an excess of small-size disks (R_d<2 kpc) is already present at z~ 0.5. The excess persists up to z~3 and involves brighter galaxies . Such an excess may be reduced if luminosity-dependent effects, like starburst activity in interacting galaxies, are included in the physical mechanisms governing the star formation history in CDM models.Comment: 9 pages, 3 figures, ApJ Letters in pres

The Evolution of the Galaxy Sizes in the NTT Deep Field: a Comparison with CDM Models

The sizes of the field galaxies with I<25 have been measured in the NTT Deep Field. Intrinsic sizes have been obtained after deconvolution of the PSF with a multigaussian method. The reliability of the method has been tested using both simulated data and HST observations of the same field. The distribution of the half light radii is peaked at r_{hl} 0.3 arcsec, in good agreement with that derived from HST images at the same magnitude. An approximate morphological classification has been obtained using the asymmetry and concentration parameters. The intrinsic sizes of the galaxies are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalog. While the brighter galaxies with morphological parameters typical of the normal spirals show a flat distribution in the range r_{d}=1-6 kpc, the fainter population at 0.4<z<0.8 dominates at small sizes. To explore the significance of this behaviour, an analytical rendition of the standard CDM model for the disc size evolution has been computed. The model showing the best fit to the local luminosity function and the Tully-Fisher relation is able to reproduce at intermediate redshifts a size distribution in general agreement with the observations, although it tends to underestimate the number of galaxies fainter than M_B~ -19 with disk sizes r_d~ 1-2 kpc.Comment: 16 pages, 11 figures, ApJ in press, Dec 199