402 research outputs found

    A Note on Tiling under Tomographic Constraints

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    Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1x1 or 1x2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or NP-complete. In this note we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.Comment: added one author and a few theorem

    Tile Packing Tomography is NP-hard

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    Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its row and column projections. It consists of disjoint copies of a fixed tile, all contained in some rectangular grid. The projections tell how many cells are covered by a tile in each row and column. How difficult is it to construct a tile packing satisfying given projections? It was known to be solvable by a greedy algorithm for bars (tiles of width or height 1), and NP-hardness results were known for some specific tiles. This paper shows that the problem is NP-hard whenever the tile is not a bar

    Optimising Spectroscopic and Photometric Galaxy Surveys: Efficient Target Selection and Survey Strategy

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    The next generation of spectroscopic surveys will have a wealth of photometric data available for use in target selection. Selecting the best targets is likely to be one of the most important hurdles in making these spectroscopic campaigns as successful as possible. Our ability to measure dark energy depends strongly on the types of targets that we are able to select with a given photometric data set. We show in this paper that we will be able to successfully select the targets needed for the next generation of spectroscopic surveys. We also investigate the details of this selection, including optimisation of instrument design and survey strategy in order to measure dark energy. We use color-color selection as well as neural networks to select the best possible emission line galaxies and luminous red galaxies for a cosmological survey. Using the Fisher matrix formalism we forecast the efficiency of each target selection scenario. We show how the dark energy figures of merit change in each target selection regime as a function of target type, survey time, survey density and other survey parameters. We outline the optimal target selection scenarios and survey strategy choices which will be available to the next generation of spectroscopic surveys.Comment: 16 pages, 22 figures, accepted to MNRAS in dec 201

    3D weak lensing with spin wavelets on the ball

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    We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analyzing of cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift information. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to bandlimited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real or harmonic space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modeling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available.Comment: 24 pages, 4 figures, version accepted for publication in PR

    Cosmological constraints on the magnification bias on sub-millimetre galaxies after large-scale bias corrections

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    Context. The study of the magnification bias produced on high-redshift sub-millimetre galaxies by foreground galaxies through the analysis of the cross-correlation function was recently demonstrated as an interesting independent alternative to the weak-lensing shear as a cosmological probe. Aims. In the case of the proposed observable, most of the cosmological constraints mainly depend on the largest angular separation measurements. Therefore, we aim to study and correct the main large-scale biases that aect foreground and background galaxy samples to produce a robust estimation of the cross-correlation function. Then we analyse the corrected signal to derive updated cosmological constraints. Methods. We measured the large-scale, bias-corrected cross-correlation functions using a background sample of H-ATLAS galaxies with photometric redshifts >1.2 and two dierent foreground samples (GAMA galaxies with spectroscopic redshifts or SDSS galaxies with photometric ones, both in the range 0.2 < z < 0.8). These measurements are modelled using the traditional halo model description that depends on both halo occupation distribution and cosmological parameters. We then estimated these parameters by performing a Markov chain Monte Carlo under multiple scenarios to study the performance of this observable and how to improve its results. Results. After the large-scale bias corrections, we obtain only minor improvements with respect to the previous magnification bias results, mainly confirming their conclusions: a lower bound on m > 0:22 at 95% CL and an upper bound 8 < 0:97 at 95% CL (results from the zspec sample). Neither the much higher surface density of the foreground photometric sample nor the assumption of Gaussian priors for the remaining unconstrained parameters significantly improve the derived constraints. However, by combining both foreground samples into a simplified tomographic analysis, we were able to obtain interesting constraints on the m8 plane as follows: m = 0:50+0:14 0:20 and 8 = 0:75+0:07 0:10 at 68% C

    Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers

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    Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers

    The reconstruction of a subclass of domino tilings from two projections

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    AbstractWe present a new way of studying the classical and still unsolved problem of the reconstruction of a domino tiling from its row and column projections. After giving a simple greedy strategy for solving the problem from one projection, we introduce the concept of degree of a domino tiling. We generalize an algorithm for the reconstruction of domino tilings of degree two from two projections, to domino tilings of degree three and four

    A Comparison of Weak Lensing Measurements From Ground- and Space-Based Facilities

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    We assess the relative merits of weak lensing surveys, using overlapping imaging data from the ground-based Subaru telescope and the Hubble Space Telescope (HST). Our tests complement similar studies undertaken with simulated data. From observations of 230,000 matched objects in the 2 square degree COSMOS field, we identify the limit at which faint galaxy shapes can be reliably measured from the ground. Our ground-based shear catalog achieves sub-percent calibration bias compared to high resolution space-based data, for galaxies brighter than i'~24.5 and with half-light radii larger than 1.8". This selection corresponds to a surface density of ~15 galaxies per sq arcmin compared to ~71 per sq arcmin from space. On the other hand the survey speed of current ground-based facilities is much faster than that of HST, although this gain is mitigated by the increased depth of space-based imaging desirable for tomographic (3D) analyses. As an independent experiment, we also reconstruct the projected mass distribution in the COSMOS field using both data sets, and compare the derived cluster catalogs with those from X-ray observations. The ground-based catalog achieves a reasonable degree of completeness, with minimal contamination and no detected bias, for massive clusters at redshifts 0.2<z<0.5. The space-based data provide improved precision and a greater sensitivity to clusters of lower mass or at higher redshift.Comment: 12 pages, 8 figures, submitted to ApJ, Higher resolution figures available at http://www.astro.caltech.edu/~mansi/GroundvsSpace.pd
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