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

Interpreting interpolation: the pattern of interpolation errors in digital surface models derived from laser scanning data

Errors within height models have, in the past, been communicated in terms of global measures ofaccuracy for the model. Such quantification ignores the spatial structure of errors across thesurface, hindering subsequent analysis. This paper demonstrates the importance ofunderstanding the spatial structure of error using, as an example, the creation of a DigitalSurface Model (DSM) from laser scanner data

Beyond Spheroids and Discs: Classifications of CANDELS Galaxy Structure at 1.4 < z < 2 via Principal Component Analysis

Important but rare and subtle processes driving galaxy morphology and star-formation may be missed by traditional spiral, elliptical, irregular or S\'ersic bulge/disk classifications. To overcome this limitation, we use a principal component analysis of non-parametric morphological indicators (concentration, asymmetry, Gini coefficient, $M_{20}$, multi-mode, intensity and deviation) measured at rest-frame $B$-band (corresponding to HST/WFC3 F125W at 1.4 $10^{10} M_{\odot}$) galaxy morphologies. Principal component analysis (PCA) quantifies the correlations between these morphological indicators and determines the relative importance of each. The first three principal components (PCs) capture $\sim$75 per cent of the variance inherent to our sample. We interpret the first principal component (PC) as bulge strength, the second PC as dominated by concentration and the third PC as dominated by asymmetry. Both PC1 and PC2 correlate with the visual appearance of a central bulge and predict galaxy quiescence. PC1 is a better predictor of quenching than stellar mass, as as good as other structural indicators (S\'ersic-n or compactness). We divide the PCA results into groups using an agglomerative hierarchical clustering method. Unlike S\'ersic, this classification scheme separates compact galaxies from larger, smooth proto-elliptical systems, and star-forming disk-dominated clumpy galaxies from star-forming bulge-dominated asymmetric galaxies. Distinguishing between these galaxy structural types in a quantitative manner is an important step towards understanding the connections between morphology, galaxy assembly and star-formation.Comment: 31 pages, 24 figures, accepted for publication in MNRA

Resampling methods for spatial regression models under a class of stochastic designs

In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs. A variant of the blocking mechanism is proposed. It is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of M-estimators of the spatial regression parameters. Finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Effect of Optic Disc Center Displacement on Retinal Nerve Fiber Layer Measurement Determined by Spectral Domain Optical Coherence Tomography

Purpose: To investigate the effect of optic disc center displacement on retinal nerve fiber layer (RNFL) measurement determined by spectral domain optical coherence tomography (SD-OCT). Methods: The optic disc center was manipulated at 1-pixel intervals in horizontal, vertical, and diagonal directions. According to the manipulated optic disc center location, the RNFL thickness data were resampled: (1) at a 3.46-mm diameter circle; and (2) between a 2.5-mm diameter circle and 5.4-mm square. Error was calculated between the original and resampled RNFL measurements. The tolerable error threshold of the optic disc center displacement was determined by considering test-retest variability of SD-OCT. The unreliable zone was defined as an area with 10% or more variability. Results: The maximum tolerable error thresholds of optic disc center displacement on the RNFL thickness map were distributed from 0.042 to 0.09 mm in 8 directions. The threshold shape was vertically elongated. Clinically important unreliable zones were located: (1) at superior and inferior region in the vertical displacement; (2) at inferotemporal region in the horizontal displacement, and (3) at superotemporal or inferotemporal region in the diagonal displacement. The unreliable zone pattern and threshold limit varied according to the direction of optic disc displacement. Conclusions: Optic disc center displacement had a considerable impact on whole RNFL thickness measurements. Understanding the effect of optic disc center displacement could contribute to reliable RNFL measurements.This study was supported by the National Research Foundation of Korea (NRF), which is funded by the Ministry of Education, Science, and Technology (no. NRF-2015R1C1A2A01053008). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Global data for ecology and epidemiology: a novel algorithm for temporal Fourier processing MODIS data

Background. Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. Methodology/Principal Findings. We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Conclusions/Significance. Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling

Highly Irregular Functional Generalized Linear Regression with Electronic Health Records

This work presents a new approach, called MISFIT, for fitting generalized functional linear regression models with sparsely and irregularly sampled data. Current methods do not allow for consistent estimation unless one assumes that the number of observed points per curve grows sufficiently quickly with the sample size. In contrast, MISFIT is based on a multiple imputation framework, which has the potential to produce consistent estimates without such an assumption. Just as importantly, it propagates the uncertainty of not having completely observed curves, allowing for a more accurate assessment of the uncertainty of parameter estimates, something that most methods currently cannot accomplish. This work is motivated by a longitudinal study on macrocephaly, or atypically large head size, in which electronic medical records allow for the collection of a great deal of data. However, the sampling is highly variable from child to child. Using MISFIT we are able to clearly demonstrate that the development of pathologic conditions related to macrocephaly is associated with both the overall head circumference of the children as well as the velocity of their head growth.Comment: 5 figures, 17 tables (including supplementary material), 34 pages (including supplementary material