23,618 research outputs found
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
The sounds of the Little and Big Bangs
Studies of heavy ion collisions have discovered that tiny fireballs of new
phase of matter -- quark gluon plasma (QGP) -- undergoes explosion, called the
Little Bang. In spite of its small size, it is not only well described by
hydrodynamics, but even small perturbations on top of the explosion turned to
be well described by hydrodynamical sound modes. The cosmological Big Bang also
went through phase transitions, the QCD and electroweak ones, which are
expected to produce sounds as well. We discuss their subsequent evolution and
hypothetical inverse acoustic cascade, amplifying the amplitude. Ultimately,
collision of two sound waves leads to formation of gravity waves, with the
smallest wavelength. We briefly discuss how those can be detected.Comment: This paper is a short semi-popular review describing some recent
developments in two very different fields, united by some common physics. It
was written for the Universe journa
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
Nonlinear unmixing of hyperspectral images: Models and algorithms
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling
Inequality, Nonhomothetic Preferences, and Trade: A Gravity Approach
In this paper, we show that inequality is an important determinant of import demand, in that it augments the standard gravity model in a significant way. We interpret this result with the aid of a model in which tastes are nonhomothetic. Classification of products, based on the correlation between household budget shares in the US and income, into "luxuries" and "necessities," works very well in our analysis when we restrict the analysis to developed importing countries. While the imports of luxuries increase with the importing country's inequality, imports of necessities decrease with it. Furthermore, we find that an increase in the level of inequality in the importing country generally leads to an increase in imports from developed countries, and to a reduction in imports from low-income countries.
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