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 $\sim20$. Using the tracking code as our reference, we show that the non-tracking codes identify complex tidal debris with purities of $\sim40$. 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 $\sim18$ of the host halo mass, which is a factor of $\sim2$ 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