87,805 research outputs found
Fast Density Codes for Image Data
Recently, a new method for encoding data sets in the form of "Density Codes"
was proposed in the literature (Courrieu, 2006). This method allows to compare
sets of points belonging to every multidimensional space, and to build shape
spaces invariant to a wide variety of affine and non-affine transformations.
However, this general method does not take advantage of the special properties
of image data, resulting in a quite slow encoding process that makes this tool
practically unusable for processing large image databases with conventional
computers. This paper proposes a very simple variant of the density code method
that directly works on the image function, which is thousands times faster than
the original Parzen window based method, without loss of its useful properties.Comment: nombre de pages:
Coordinate-Space Hartree-Fock-Bogoliubov Description of Superfluid Fermi Systems
Properties of strongly interacting, two-component finite Fermi systems are
discussed within the recently developed coordinate-space
Hartree-Fock-Bogoliubov (HFB) code {\hfbax}. Two illustrative examples are
presented: (i) weakly bound deformed Mg isotopes, and (ii) spin-polarized
atomic condensates in a strongly deformed harmonic trap.Comment: 4 pages, 2 figures, ENAM 2008 conference proceedings (EPJA
Numerical estimation of densities
[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the
underlying density field from a discrete set of sample points in an arbitrary
multidimensional space. FiEstAS assigns a volume to each point by means of a
binary tree. Density is then computed by integrating over an adaptive kernel.
As a first test, we construct several Monte Carlo realizations of a Hernquist
profile and recover the particle density in both real and phase space. At a
given point, Poisson noise causes the unsmoothed estimates to fluctuate by a
factor ~2 regardless of the number of particles. This spread can be reduced to
about 1 dex (~26 per cent) by our smoothing procedure. [...] We conclude that
our algorithm accurately measure the phase-space density up to the limit where
discreteness effects render the simulation itself unreliable. Computationally,
FiEstAS is orders of magnitude faster than the method based on Delaunay
tessellation that Arad et al. employed, making it practicable to recover
smoothed density estimates for sets of 10^9 points in 6 dimensions.Comment: 12 pages, 18 figures, submitted to MNRAS. The code is available upon
reques
Semidefinite programming, harmonic analysis and coding theory
These lecture notes where presented as a course of the CIMPA summer school in
Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics.
This version is an update June 2010
Streams Going Notts: The tidal debris finder comparison project
While various codes exist to systematically and robustly find haloes and
subhaloes in cosmological simulations (Knebe et al., 2011, Onions et al.,
2012), this is the first work to introduce and rigorously test codes that find
tidal debris (streams and other unbound substructure) in fully cosmological
simulations of structure formation. We use one tracking and three non-tracking
codes to identify substructure (bound and unbound) in a Milky Way type
simulation from the Aquarius suite (Springel et al., 2008) and post-process
their output with a common pipeline to determine the properties of these
substructures in a uniform way. By using output from a fully cosmological
simulation, we also take a step beyond previous studies of tidal debris that
have used simple toy models. We find that both tracking and non-tracking codes
agree well on the identification of subhaloes and more importantly, the {\em
unbound tidal features} associated with them. The distributions of basic
properties of the total substructure distribution (mass, velocity dispersion,
position) are recovered with a scatter of . Using the tracking code as
our reference, we show that the non-tracking codes identify complex tidal
debris with purities of . Analysing the results of the substructure
finders, we find that the general distribution of {\em substructures} differ
significantly from the distribution of bound {\em subhaloes}. Most importantly,
both bound and unbound {\em substructures} together constitute of the
host halo mass, which is a factor of higher than the fraction in
self-bound {\em subhaloes}. However, this result is restricted by the remaining
challenge to cleanly define when an unbound structure has become part of the
host halo. Nevertheless, the more general substructure distribution provides a
more complete picture of a halo's accretion history.Comment: 19 pages, 12 figures, accepted for publication in MNRA
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
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