Some criteria for determining recognizability of a set

Let an be the number of strings of length n in a set A ⊆ ∑*, where ∑ is a finite alphabet. Several criteria for determining that a set is not recognizable by a finite automaton are given, based solely on the sequence {an}. The sequence {an} is also used to define a finitely addititive probability measure on all recognizable sets

Galactic Extinction from Colors and Counts of Field Galaxies in WFPC2 Frames: An Application to GRB 970228

We develop the ``simulated extinction method'' to measure average foreground Galactic extinction from field galaxy number-counts and colors. The method comprises simulating extinction in suitable reference fields by changing the isophotal detection limit. This procedure takes into account selection effects, in particular, the change in isophotal detection limit (and hence in isophotal magnitude completeness limit) with extinction, and the galaxy color--magnitude relation. We present a first application of the method to the HST WFPC2 images of the gamma-ray burster GRB 970228. Four different WFPC2 high-latitude fields, including the HDF, are used as reference to measure the average extinction towards the GRB in the F606W passband. From the counts, we derive an average extinction of A_V = 0.5 mag, but the dispersion of 0.4 mag between the estimates from the different reference fields is significantly larger than can be accounted by Poisson plus clustering uncertainties. Although the counts differ, the average colors of the field galaxies agree well. The extinction implied by the average color difference between the GRB field and the reference galaxies is A_V = 0.6 mag, with a dispersion in the estimated extinction from the four reference fields of only 0.1 mag. All our estimates are in good agreement with the value of 0.81\pm0.27 mag obtained by Burstein & Heiles, and with the extinction of 0.78\pm0.12 measured by Schlegel et al. from maps of dust IR emission. However, the discrepancy between the widely varying counts and the very stable colors in these high-latitude fields is worth investigating.Comment: 14 pages, 2 figures; submitted to the Astrophysical Journa

Faint K Selected Galaxy Correlations and Clustering Evolution

Angular and spatial correlations are measured for K-band--selected galaxies, 248 having redshifts, 54 with z>1, in two patches of combined area 27 arcmin^2. The angular correlation for K<=21.5 mag is (theta/1.4+/-0.19 arcsec e^{+/-0.1})^{-0.8}. From the redshift sample we find that the real-space correlation, calculated with q_0=0.1, of M_K<=-23.5 mag galaxies (k-corrected) is \xi(r) = (r/2.9e^{+/-0.12}1/h Mpc)^{-1.8} at a mean z= 0.34, (r/2.0e^{+/-0.15}1/h Mpc)^{-1.8} at z= 0.62, (r/1.4e^{+/-0.15}1/h Mpc)^{-1.8} at z= 0.97, and (r/1.0e^{+/-0.2}1/h Mpc)^{-1.8} at z= 1.39, the last being a formal upper limit for a blue-biased sample. In general, these are more correlated than optically selected samples in the same redshift ranges. Over the interval 0.32 AB mag, have \xi(r)=(r/2.4e^{+/-0.14}1/h Mpc)^{-1.8} whereas bluer galaxies, which have a mean B of 23.7 mag and mean [OII] equivalent width W_{eq} = 41=\AA, are very weakly correlated, with \xi(r)=(r/0.9e^{+/-0.22}1/h Mpc)^{-1.8}. For our measured growth rate of clustering, this blue population, if non-merging, can grow only into a low-redshift population less luminous than 0.4L_\ast. The cross-correlation of low- and high-luminosity galaxies at z=0.6 appears to have an excess in the correlation amplitude within 100/h kpc. The slow redshift evolution is consistent with these galaxies tracing the mass clustering in low density, Omega= 0.2, relatively unbiased, sigma_8=0.8, universe, but cannot yet exclude other possibilities.Comment: to be published in the Aug 1 ApJ, 20 pages as a uuencoded postscript file Postscript with all figures is available at http://manaslu.astro.utoronto.ca/~carlberg/paper

The distortion of distant galaxy images by large-scale structure

Inhomogeneity in the distribution of mass in the universe on scales ≲ 100 Mpc can generate a coherent shear distortion or polarization of the images of background galaxies. This distortion may be measurable over patches of the sky up to a few square degrees in size. If this distortion is measured, or conversely, if its magnitude is limited, it should help us understand the degree to which luminosity traces the underlying mass over cosmological scales. A prescription is given for quantifying the galaxy distortion and a propagation equation for its evolution in an inhomogeneous universe is derived. The creation of shear by inhomogeneity is illustrated using model kinematic universes comprising random distributions of point masses, spheres and circular discs designed to simulate the superclusters, voids and ‘walls’ reported in galaxy velocity surveys. Using these simulations, we estimate that an rms induced ellipticity of |p|_(rms) ˜ 0.2Ω_(LSS) (where Ω_(LSS) is the fraction of the mass of the universe clustered on the large scale) will be produced. The angular correlation length is ˜ 1.6°. In an alternative prescription, the universe is modelled using a power spectrum of density fluctuations and the mean correlation function is computed both analytically and numerically. In these simulations we find that |p|_(rms) ˜0.02 for biased cold dark matter models of an Einslein–De Sitter universe, and the effective correlation length is θ_(1/2) ˜ 0.5^ΰ. For a hot dark matter dominated universe the correlation length is θ_(1/2) ˜ 0.7^ΰ. The faint, blue galaxies discovered by Tyson and collaborators have a surface density of ˜ 3 × 10^5 deg^(−2) and should provide an ideal set of sources for measuring this effect

XROMM analysis of tooth occlusion and temporomandibular joint kinematics during feeding in juvenile miniature pigs

Like humans, domestic pigs are omnivorous and thus are a common model for human masticatory function. Prior attempts to characterize food–tooth interactions and jaw movements associated with mastication have been limited to aspects of the oral apparatus that are visible externally (with videography) and/or to 2D movements of oral structures (with monoplanar videofluoroscopy). We used XROMM, a 3D technique that combines CT-based morphology with biplanar videofluoroscopy, to quantify mandibular kinematics, tooth occlusion and mandibular condylar displacements within the temporomandibular joint (TMJ) during feeding. We observed that the pig TMJ moved detectably in only three of six possible degrees of freedom during mastication: two rotations, pitch and yaw; and one translation, protraction–retraction. Asymmetrical yaw around a dorsoventral axis produced the observed alternating left–right chewing cycles responsible for food reduction. Furthermore, the relative motions of the upper and lower premolars contained a substantial mesiodistal component in addition to the buccolingual component, resulting in an oblique (rather than a strictly transverse) power stroke. This research demonstrates the capacity of XROMM to explore the kinematic underpinnings of key masticatory movements, such as the occlusal power stroke, by integrating tooth, joint and rigid body jaw movements. XROMM also allowed us to test kinematic hypotheses based on skeletal anatomy with actual kinematics observed during naturalistic feeding behaviors. We observed that the soft tissue structures of the TMJ appear to play a significant role in limiting the range of motion of a joint, and thus analyses based solely on osseous morphology may over-estimate joint mobility

Measuring the Angular Correlation Function for Faint Galaxies in High Galactic Latitude Fields

A photometric survey of faint galaxies in three high Galactic latitude fields (each $\sim49~\rm{arcmin^{2}}$) with sub-arcsecond seeing is used to study the clustering properties of the faint galaxy population. Multi-color photometry of the galaxies has been obtained to magnitude limits of $V\sim25$, $R\sim25$ and $I\sim24$. Angular correlation analysis is applied to magnitude-limited and color-selected samples of galaxies from the three fields for angular separations ranging from $10-126''$. General agreement is obtained with other recent studies which show that the amplitude of the angular correlation function, $\omega(\theta)$, is smoothly decreasing as a function of limiting magnitude. The observed decline of $\omega(\theta)$ rules out the viability of ``maximal merger'' galaxy evolution models. Using redshift distributions extrapolated to faint magnitude limits, models of galaxy clustering evolution are calculated and compared to the observed I-band $\omega(\theta)$. Faint galaxies are determined to have correlation lengths and clustering evolution parameters of either $r_{0}\sim4~h^{-1}~Mpc$ and $\epsilon\sim0-1$; $r_{0}\sim5-6~h^{-1}~Mpc$ and $\epsilon>1$; or $r_{0}\sim2-3~h^{-1}~ Mpc$ and $\epsilon\sim-1.2$, assuming $q_{0}=0.5$ and with $h=H_{0}/100~ km~s^{-1}~Mpc^{-1}$. The latter case is for clustering fixed in co-moving coordinates and is probably unrealistic since most local galaxies are observed to be more strongly clustered. No significant variations in the clustering amplitude as a function of color are detected, for all the color-selected galaxy samples considered. (Abridged)Comment: LaTeX (aaspp4.sty), 54 pages including 15 postscript figures; 3 additional uuencoded, gzipped postscript files (~300 kb each) of Figs. 1, 2 and 3 available at ftp://ftp.astro.ubc.ca/pub/woods ; To be published in the Nov. 20, 1997 issue of The Astrophysical Journa

The non-Gaussian tail of cosmic-shear statistics

Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of high-redshift galaxy images due to the tidal gravitational field of the large-scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the LSS. In particular, non-Gaussian properties of the LSS will lead to a non-Gaussian distribution of cosmic-shear statistics. The aperture mass ($M_{\rm ap}$) statistics, recently introduced as a measure for cosmic shear, is particularly well suited for measuring these non-Gaussian properties. In this paper we calculate the highly non-Gaussian tail of the aperture mass probability distribution, assuming Press-Schechter theory for the halo abundance and the `universal' density profile of haloes as obtained from numerical simulations. We find that for values of $M_{\rm ap}$ much larger than its dispersion, this probability distribution is closely approximated by an exponential, rather than a Gaussian. We determine the amplitude and shape of this exponential for various cosmological models and aperture sizes, and show that wide-field imaging surveys can be used to distinguish between some of the currently most popular cosmogonies. Our study here is complementary to earlier cosmic-shear investigations which focussed more on two-point statistical properties.Comment: 9 pages, 5 figures, submitted to MNRA

Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Cosmic Shear from STIS Pure Parallels: Analysis

The measurement of cosmic shear requires deep imaging with high image quality on many lines of sight to sample the statistics of large-scale structure. The expected distortion of galaxy images by cosmic shear on the STIS angular scale is a few percent, therefore the PSF anisotropy has to be understood and controlled to an accuracy better than 1%. In this poster we present the analysis of the PSF of STIS and a preliminary cosmic shear measurement using archival data from the STIS pure parallel program to show that the STIS camera on-board HST is well suited for our project. The data reduction and catalog production are described in an accompanying paper (astro-ph/0102330).Comment: 4 pages, 5 figures, to appear in the proceedings of the STScI 2001 spring symposium "The Dark Universe: Matter, Energy and Gravity" Baltimore April 2-5 2001, acknowledgements adde

Cold collapse and the core catastrophe

We show that a universe dominated by cold dark matter fails to reproduce the rotation curves of dark matter dominated galaxies, one of the key problems that it was designed to resolve. We perform numerical simulations of the formation of dark matter halos, each containing \gsim 10^6 particles and resolved to 0.003 times the virial radius, allowing an accurate comparison with rotation curve data. A good fit to both galactic and cluster sized halos can be achieved using the density profile rho(r) \propto [(r/r_s)^1.5(1+(r/r_s)^1.5)]^-1, where r_s is a scale radius. This profile has a steeper asymptotic slope, rho(r) \propto r^-1.5, and a sharper turnover than found by lower resolution studies. The central structure of relaxed halos that form within a hierarchical universe has a remarkably small scatter (unrelaxed halos would not host disks). We compare the results with a sample of dark matter dominated, low surface brightness (LSB) galaxies with circular velocities in the range 100-300 km/s. The rotation curves of disks within cold dark matter halos rise too steeply to match these data which require a constant mass density in the central regions. The same conclusion is reached if we compare the scale free shape of observed rotation curves with the simulation data. It is important to confirm these results using stellar rather than HI rotation curves for LSB galaxies. We test the effects of introducing a cut-off in the power spectrum that may occur in a universe dominated by warm dark matter. In this case halos form by a monolithic collapse but the final density profile hardly changes, demonstrating that the merger history does not play a role in determining the halo structure.Comment: Latex 13 pages, 4 figures. Submitted to MNRAS. High resolution colour version of figure 4 and other N-body images here: http://star-www.dur.ac.uk:80/~moore/images