POTENT Reconstruction from Mark III Velocities

We present an improved POTENT method for reconstructing the velocity and mass density fields from radial peculiar velocities, test it with mock catalogs, and apply it to the Mark III Catalog. Method improvments: (a) inhomogeneous Malmquist bias is reduced by grouping and corrected in forward or inverse analyses of inferred distances, (b) the smoothing into a radial velocity field is optimized to reduce window and sampling biases, (c) the density is derived from the velocity using an improved nonlinear approximation, and (d) the computational errors are made negligible. The method is tested and optimized using mock catalogs based on an N-body simulation that mimics our cosmological neighborhood, and the remaining errors are evaluated quantitatively. The Mark III catalog, with ~3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 Mpc/h out to ~60 Mpc/h. We present maps of the 3D velocity and mass-density fields and the corresponding errors. The typical systematic and random errors in the density fluctuations inside 40 Mpc/h are \pm 0.13 and \pm 0.18. The recovered mass distribution resembles in its gross features the galaxy distribution in redshift surveys and the mass distribution in a similar POTENT analysis of a complementary velocity catalog (SFI), including the Great Attractor, Perseus-Pisces, and the void in between. The reconstruction inside ~40 Mpc/h is not affected much by a revised calibration of the distance indicators (VM2, tailored to match the velocities from the IRAS 1.2Jy redshift survey). The bulk velocity within the sphere of radius 50 Mpc/h about the Local Group is V_50=370 \pm 110 km/s (including systematic errors), and is shown to be mostly generated by external mass fluctuations. With the VM2 calibration, V_50 is reduced to 305 \pm 110 km/s.Comment: 60 pages, LaTeX, 3 tables and 27 figures incorporated (may print the most crucial figures only, by commenting out one line in the LaTex source

The LSST DESC data challenge 1: Generation and analysis of synthetic images for next-generation surveys

Data Challenge 1 (DC1) is the first synthetic data set produced by the Rubin Observatory Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC). DC1 is designed to develop and validate data reduction and analysis and to study the impact of systematic effects that will affect the LSST data set. DC1 is comprised of r-band observations of 40 deg2 to 10 yr LSST depth. We present each stage of the simulation and analysis process: (a) generation, by synthesizing sources from cosmological N-body simulations in individual sensor-visit images with different observing conditions; (b) reduction using a development version of the LSST Science Pipelines; and (c) matching to the input cosmological catalogue for validation and testing. We verify that testable LSST requirements pass within the fidelity of DC1. We establish a selection procedure that produces a sufficiently clean extragalactic sample for clustering analyses and we discuss residual sample contamination, including contributions from inefficiency in star-galaxy separation and imperfect deblending. We compute the galaxy power spectrum on the simulated field and conclude that: (i) survey properties have an impact of 50 per cent of the statistical uncertainty for the scales and models used in DC1; (ii) a selection to eliminate artefacts in the catalogues is necessary to avoid biases in the measured clustering; and (iii) the presence of bright objects has a significant impact (2-6) in the estimated power spectra at small scales (> 1200), highlighting the impact of blending in studies at small angular scales in LSST

Optimization of Planck/LFI on--board data handling

To asses stability against 1/f noise, the Low Frequency Instrument (LFI) onboard the Planck mission will acquire data at a rate much higher than the data rate allowed by its telemetry bandwith of 35.5 kbps. The data are processed by an onboard pipeline, followed onground by a reversing step. This paper illustrates the LFI scientific onboard processing to fit the allowed datarate. This is a lossy process tuned by using a set of 5 parameters Naver, r1, r2, q, O for each of the 44 LFI detectors. The paper quantifies the level of distortion introduced by the onboard processing, EpsilonQ, as a function of these parameters. It describes the method of optimizing the onboard processing chain. The tuning procedure is based on a optimization algorithm applied to unprocessed and uncompressed raw data provided either by simulations, prelaunch tests or data taken from LFI operating in diagnostic mode. All the needed optimization steps are performed by an automated tool, OCA2, which ends with optimized parameters and produces a set of statistical indicators, among them the compression rate Cr and EpsilonQ. For Planck/LFI the requirements are Cr = 2.4 and EpsilonQ <= 10% of the rms of the instrumental white noise. To speedup the process an analytical model is developed that is able to extract most of the relevant information on EpsilonQ and Cr as a function of the signal statistics and the processing parameters. This model will be of interest for the instrument data analysis. The method was applied during ground tests when the instrument was operating in conditions representative of flight. Optimized parameters were obtained and the performance has been verified, the required data rate of 35.5 Kbps has been achieved while keeping EpsilonQ at a level of 3.8% of white noise rms well within the requirements.Comment: 51 pages, 13 fig.s, 3 tables, pdflatex, needs JINST.csl, graphicx, txfonts, rotating; Issue 1.0 10 nov 2009; Sub. to JINST 23Jun09, Accepted 10Nov09, Pub.: 29Dec09; This is a preprint, not the final versio

Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively studied for more than two decades, resulting in various extensions to the original technique and beautiful algorithms for a wide range of applications. Despite the fact that this approach yields tight approximation guarantees for some problems, e.g., Max-Cut, for many others, e.g., Max-SAT and Max-DiCut, the tight approximation ratio is still unknown. One of the main reasons for this is the fact that very few techniques for rounding semidefinite relaxations are known. In this work, we present a new general and simple method for rounding semi-definite programs, based on Brownian motion. Our approach is inspired by recent results in algorithmic discrepancy theory. We develop and present tools for analyzing our new rounding algorithms, utilizing mathematical machinery from the theory of Brownian motion, complex analysis, and partial differential equations. Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut, Max-2SAT, and MaxDiCut, and derive new algorithms that are competitive with the best known results. To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration results for the Sticky Brownian Motion, a feature missing from hyperplane rounding and its generalization