239 research outputs found
A Note on Tiling under Tomographic Constraints
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
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
Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias
Aims: The main goal of this paper is to derive observational constraints on the halo mass fuction (HMF) by performing a tomographic analysis of the magnification bias signal on a sample of background submillimeter galaxies. The results can then be compared with those from a non-tomographic study.
Methods: We measure the cross-correlation function between a sample of foreground GAMA galaxies with spectroscopic redshifts in the range 0.1 < z < 0.8 (and divided up into four bins) and a sample of background submillimeter galaxies from H-ATLAS with photometric redshifts in the range 1.2 < z < 4.0. We model the weak lensing signal within the halo model formalism and carry out a Markov chain Monte Carlo algorithm to obtain the posterior distribution of all HMF parameters, which we assume to follow the Sheth and Tormen (ST) three-parameter and two-parameter fits.
Results: While the observational constraints on the HMF from the non-tomographic analysis are not stringent, there is a remarkable improvement in terms of uncertainty reduction when tomography is adopted. Moreover, with respect to the traditional ST triple of values from numerical simulations, the results from the three-parameter fit predict a higher number density of halos at masses below ∼1012 M⊙ h−1 at 95% credibility. The two-parameter fit yields even more restricting results, with a larger number density of halos below ∼1013 M⊙ h−1 and a lower one above ∼1014 M⊙ h−1, this time at more than 3σ credibility. Our results are therefore in disagreement with the standard N-body values for the ST fit at 2σ and 3σ, respectively
Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers
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
Cosmological constraints on the magnification bias on sub-millimetre galaxies after large-scale bias corrections
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
The reconstruction of a subclass of domino tilings from two projections
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
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
Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space
We present constraints on local primordial non-Gaussianity (PNG),
parametrized through , using the Sloan Digital Sky Survey
IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar
sample. We measure and analyze the anisotropic clustering of the quasars in
Fourier space, testing for the scale-dependent bias introduced by primordial
non-Gaussianity on large scales. We derive and employ a power spectrum
estimator using optimal weights that account for the redshift evolution of the
PNG signal. We find constraints of at 95%
confidence level. These are amont the tightest constraints from Large Scale
Structure (LSS) data. Our redshift weighting improves the error bar by 15% in
comparison to the unweighted case. If quasars have lower response to PNG, the
constraint degrades to , with a 40% improvement
over the standard approach. We forecast that the full eBOSS dataset could reach
using optimal methods and full
range of scales.Comment: 28 pages, 12 figures. Comments welcome
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