20,400 research outputs found
Hardware Based Projection onto The Parity Polytope and Probability Simplex
This paper is concerned with the adaptation to hardware of methods for
Euclidean norm projections onto the parity polytope and probability simplex. We
first refine recent efforts to develop efficient methods of projection onto the
parity polytope. Our resulting algorithm can be configured to have either
average computational complexity or worst case
complexity on a serial processor where
is the dimension of projection space. We show how to adapt our projection
routine to hardware. Our projection method uses a sub-routine that involves
another Euclidean projection; onto the probability simplex. We therefore
explain how to adapt to hardware a well know simplex projection algorithm. The
hardware implementations of both projection algorithms achieve area scalings of
at a delay of
. Finally, we present numerical results in
which we evaluate the fixed-point accuracy and resource scaling of these
algorithms when targeting a modern FPGA
LP-decodable multipermutation codes
In this paper, we introduce a new way of constructing and decoding
multipermutation codes. Multipermutations are permutations of a multiset that
may consist of duplicate entries. We first introduce a new class of matrices
called multipermutation matrices. We characterize the convex hull of
multipermutation matrices. Based on this characterization, we propose a new
class of codes that we term LP-decodable multipermutation codes. Then, we
derive two LP decoding algorithms. We first formulate an LP decoding problem
for memoryless channels. We then derive an LP algorithm that minimizes the
Chebyshev distance. Finally, we show a numerical example of our algorithm.Comment: This work was supported by NSF and NSERC. To appear at the 2014
Allerton Conferenc
Efficient learning of neighbor representations for boundary trees and forests
We introduce a semiparametric approach to neighbor-based classification. We
build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015)
which enables fast neighbor-based classification, regression and retrieval in
large datasets. While boundary trees use an Euclidean measure of similarity,
the Differentiable Boundary Tree algorithm by Zoran et al.(2017) was introduced
to learn low-dimensional representations of complex input data, on which
semantic similarity can be calculated to train boundary trees. As is pointed
out by its authors, the differentiable boundary tree approach contains a few
limitations that prevents it from scaling to large datasets. In this paper, we
introduce Differentiable Boundary Sets, an algorithm that overcomes the
computational issues of the differentiable boundary tree scheme and also
improves its classification accuracy and data representability. Our algorithm
is efficiently implementable with existing tools and offers a significant
reduction in training time. We test and compare the algorithms on the well
known MNIST handwritten digits dataset and the newer Fashion-MNIST dataset by
Xiao et al.(2017).Comment: 9 pages, 2 figure
Collisionless distribution function for the relativistic force-free Harris sheet
A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]PostprintPeer reviewe
Dust cloud evolution in sub-stellar atmospheres via plasma deposition and plasma sputtering
Context. In contemporary sub-stellar model atmospheres, dust growth occurs through neutral gas-phase surface chemistry. Recently, there has been a growing body of theoretical and observational evidence suggesting that ionisation processes can also occur. As a result, atmospheres are populated by regions composed of plasma, gas and dust, and the consequent influence of plasma processes on dust evolution is enhanced.Aim. This paper aims to introduce a new model of dust growth and destruction in sub-stellar atmospheres via plasma deposition and plasma sputtering.Methods. Using example sub-stellar atmospheres from DRIFT-PHOENIX, we have compared plasma deposition and sputtering timescales to those from neutral gas-phase surface chemistry to ascertain their regimes of influence. We calculated the plasma sputtering yield and discuss the circumstances where plasma sputtering dominates over deposition.Results. Within the highest dust density cloud regions, plasma deposition and sputtering dominates over neutral gas-phase surface chemistry if the degree of ionisation is ≳10−4. Loosely bound grains with surface binding energies of the order of 0.1–1 eV are susceptible to destruction through plasma sputtering for feasible degrees of ionisation and electron temperatures; whereas, strong crystalline grains with binding energies of the order 10 eV are resistant to sputtering.Conclusions. The mathematical framework outlined sets the foundation for the inclusion of plasma deposition and plasma sputtering in global dust cloud formation models of sub-stellar atmospheres
Collisional Grooming Models of the Kuiper Belt Dust Cloud
We modeled the 3-D structure of the Kuiper Belt dust cloud at four different
dust production rates, incorporating both planet-dust interactions and
grain-grain collisions using the collisional grooming algorithm. Simulated
images of a model with a face-on optical depth of ~10^-4 primarily show an
azimuthally-symmetric ring at 40-47 AU in submillimeter and infrared
wavelengths; this ring is associated with the cold classical Kuiper Belt. For
models with lower optical depths (10^-6 and 10^-7), synthetic infrared images
show that the ring widens and a gap opens in the ring at the location of of
Neptune; this feature is caused by trapping of dust grains in Neptune's mean
motion resonances. At low optical depths, a secondary ring also appears
associated with the hole cleared in the center of the disk by Saturn. Our
simulations, which incorporate 25 different grain sizes, illustrate that
grain-grain collisions are important in sculpting today's Kuiper Belt dust, and
probably other aspects of the Solar System dust complex; collisions erase all
signs of azimuthal asymmetry from the submillimeter image of the disk at every
dust level we considered. The model images switch from being dominated by
resonantly-trapped small grains ("transport dominated") to being dominated by
the birth ring ("collision dominated") when the optical depth reaches a
critical value of tau ~ v/c, where v is the local Keplerian speed.Comment: 31 pages, including 9 figure
The impact of M-dwarf atmosphere modelling on planet detection
Being able to accurately estimate stellar parameters based on spectral
observations is important not only for understanding the stars themselves but
it is also vital for the determination of exoplanet parameters. M dwarfs are
discussed as targets for planet detection as these stars are less massive, less
luminous and have smaller radii making it possible to detect smaller and
lighter planets. Therefore M-dwarfs could prove to be a valuable source for
examining the lower mass end of planet distribution, but in order to do that,
one must first take care to understand the characteristics of the host stars
well enough. Up to date, there are several families of stellar model
atmospheres. We focus on the ATLAS9, MARCS and Drift-Phoenix families in the
M-dwarf parameter space. We examine the differences in the (Tgas, pgas)
structures, synthetic photometric fluxes and related colour indices.We find
discrepancies in the hotter regions of the stellar atmosphere between the ATLAS
and MARCS models. The MARCS and Drift-Phoenix models appear to agree to a
better extend with variances of less than 300K. We have compiled the broad-band
synthetic photometric fluxes of all models for the Johnson UBVRI and 2MASS
JHKs. The fluxes of MARCS differ from both ATLAS and Drift-Phoenix models in
the optical range.Comment: submitted to the proceedings of the conference 'Brown dwarfs come of
age', May 20-24 2013, Memorie della Societa Astronomica Italian
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