21,449 research outputs found
Social Percolation and the Influence of Mass Media
Mass media shift the percolative phase transition observed in the marketing
model of Solomon and Weisbuch.Comment: 6 pages including 4 figure
Reply to Comment: Quantum Cryptography Based on Orthogonal States?
This is our Reply to Peres' Comment [quant-ph/9509003] to "Quantum
Cryptography Based on Orthogonal States" [Phys. Rev. Lett. 75, 1239 (1995)].Comment: 3 pages, LaTex, no figure
Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
We examine LDPC codes decoded using linear programming (LP). Four
contributions to the LP framework are presented. First, a new method of
tightening the LP relaxation, and thus improving the LP decoder, is proposed.
Second, we present an algorithm which calculates a lower bound on the minimum
distance of a specific code. This algorithm exhibits complexity which scales
quadratically with the block length. Third, we propose a method to obtain a
tight lower bound on the fractional distance, also with quadratic complexity,
and thus less than previously-existing methods. Finally, we show how the
fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can
be obtained.Comment: 17 pages, 8 figures, Submitted to IEEE Transactions on Information
Theor
On the Microscopic Foundations of Elasticity
The modeling of the elastic properties of disordered or nanoscale solids
requires the foundations of the theory of elasticity to be revisited, as one
explores scales at which this theory may no longer hold. The only cases for
which microscopically based derivations of elasticity are documented are
(nearly) uniformly strained lattices. A microscopic approach to elasticity is
proposed. As a first step, microscopically exact expressions for the
displacement, strain and stress fields are derived. Conditions under which
linear elastic constitutive relations hold are studied theoretically and
numerically. It turns out that standard continuum elasticity is not
self-evident, and applies only above certain spatial scales, which depend on
details of the considered system and boundary conditions. Possible relevance to
granular materials is briefly discussed.Comment: 6 pages, 5 figures, LaTeX2e with svjour.cls and svepj.clo, submitted
to EPJ E, minor error corrected in v
Small and Large Scale Granular Statics
Recent experimental results on the static or quasistatic response of granular
materials have been interpreted to suggest the inapplicability of the
traditional engineering approaches, which are based on elasto-plastic models
(which are elliptic in nature). Propagating (hyperbolic) or diffusive
(parabolic) models have been proposed to replace the `old' models. Since
several recent experiments were performed on small systems, one should not
really be surprised that (continuum) elasticity, a macroscopic theory, is not
directly applicable, and should be replaced by a grain-scale (``microscopic'')
description. Such a description concerns the interparticle forces, while a
macroscopic description is given in terms of the stress field. These
descriptions are related, but not equivalent, and the distinction is important
in interpreting the experimental results. There are indications that at least
some large scale properties of granular assemblies can be described by
elasticity, although not necessarily its isotropic version. The purely
repulsive interparticle forces (in non-cohesive materials) may lead to
modifications of the contact network upon the application of external forces,
which may strongly affect the anisotropy of the system. This effect is expected
to be small (in non-isostatic systems) for small applied forces and for
pre-stressed systems (in particular for disordered systems). Otherwise, it may
be accounted for using a nonlinear, incrementally elastic model, with
stress-history dependent elastic moduli. Although many features of the
experiments may be reproduced using models of frictionless particles, results
demonstrating the importance of accounting for friction are presented.Comment: 10 pages, 9 figures. Accepted for publication in "Granular Matter"
(special issue: 4th Int. Conf. on Conveying and Handling of Particulate
Solids, Budapest, Hungary, May 2003). v2: Minor revisions to text and figure
Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations
This paper is focused on the performance analysis of binary linear block
codes (or ensembles) whose transmission takes place over independent and
memoryless parallel channels. New upper bounds on the maximum-likelihood (ML)
decoding error probability are derived. These bounds are applied to various
ensembles of turbo-like codes, focusing especially on repeat-accumulate codes
and their recent variations which possess low encoding and decoding complexity
and exhibit remarkable performance under iterative decoding. The framework of
the second version of the Duman and Salehi (DS2) bounds is generalized to the
case of parallel channels, along with the derivation of their optimized tilting
measures. The connection between the generalized DS2 and the 1961 Gallager
bounds, addressed by Divsalar and by Sason and Shamai for a single channel, is
explored in the case of an arbitrary number of independent parallel channels.
The generalization of the DS2 bound for parallel channels enables to re-derive
specific bounds which were originally derived by Liu et al. as special cases of
the Gallager bound. In the asymptotic case where we let the block length tend
to infinity, the new bounds are used to obtain improved inner bounds on the
attainable channel regions under ML decoding. The tightness of the new bounds
for independent parallel channels is exemplified for structured ensembles of
turbo-like codes. The improved bounds with their optimized tilting measures
show, irrespectively of the block length of the codes, an improvement over the
union bound and other previously reported bounds for independent parallel
channels; this improvement is especially pronounced for moderate to large block
lengths.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages,
9 figures
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