3,762 research outputs found
Resampling methods for document clustering
We compare the performance of different clustering algorithms applied to the
task of unsupervised text categorization. We consider agglomerative clustering
algorithms, principal direction divisive partitioning and (for the first time)
superparamagnetic clustering with several distance measures. The algorithms
have been applied to test databases extracted from the Reuters-21578 text
categorization test database. We find that simple application of the different
clustering algorithms yields clustering solutions of comparable quality. In
order to achieve considerable improvements of the clustering results it is
crucial to reduce the dictionary of words considered in the representation of
the documents. Significant improvements of the quality of the clustering can be
obtained by identifying discriminative words and filtering out indiscriminative
words from the dictionary. We present two methods, each based on a resampling
scheme, for selecting discriminative words in an unsupervised way.Comment: RevTeX, 9 pages, 2 figure
Improving convergence of Belief Propagation decoding
The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP)
algorithm is revisited. We check the iterative algorithm for its convergence to
a codeword (termination), we run Monte Carlo simulations to find the
probability distribution function of the termination time, n_it. Tested on an
example [155, 64, 20] code, this termination curve shows a maximum and an
extended algebraic tail at the highest values of n_it. Aiming to reduce the
tail of the termination curve we consider a family of iterative algorithms
modifying the standard BP by means of a simple relaxation. The relaxation
parameter controls the convergence of the modified BP algorithm to a minimum of
the Bethe free energy. The improvement is experimentally demonstrated for
Additive-White-Gaussian-Noise channel in some range of the signal-to-noise
ratios. We also discuss the trade-off between the relaxation parameter of the
improved iterative scheme and the number of iterations
New Bisoltion Solutions in Dispersion Managed Systems
In this paper we propose a method which provides a full description of
solitary wave solutions of the Schroedinger equation with periodically varying
dispersion. This method is based on analysis and polynomial deformation of the
spectrum of an iterative map. Using this method we discover a new family of
antisymmetric bisoliton solutions. In addition to the fact that these solutions
are of interest for nonlinear fiber optics and the theory of nonlinear
Schroedinger equations with periodic coefficients, they have potential
applications for increasing of bit-rate in high speed optical fiber
communications
An Efficient Pseudo-Codeword Search Algorithm for Linear Programming Decoding of LDPC Codes
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code
one minimizes a linear functional, with coefficients related to log-likelihood
ratios, over a relaxation of the polytope spanned by the codewords
\cite{03FWK}. In order to quantify LP decoding, and thus to describe
performance of the error-correction scheme at moderate and large
Signal-to-Noise-Ratios (SNR), it is important to study the relaxed polytope to
understand better its vertexes, so-called pseudo-codewords, especially those
which are neighbors of the zero codeword. In this manuscript we propose a
technique to heuristically create a list of these neighbors and their
distances. Our pseudo-codeword-search algorithm starts by randomly choosing the
initial configuration of the noise. The configuration is modified through a
discrete number of steps. Each step consists of two sub-steps. Firstly, one
applies an LP decoder to the noise-configuration deriving a pseudo-codeword.
Secondly, one finds configuration of the noise equidistant from the pseudo
codeword and the zero codeword. The resulting noise configuration is used as an
entry for the next step. The iterations converge rapidly to a pseudo-codeword
neighboring the zero codeword. Repeated many times, this procedure is
characterized by the distribution function (frequency spectrum) of the
pseudo-codeword effective distance. The effective distance of the coding scheme
is approximated by the shortest distance pseudo-codeword in the spectrum. The
efficiency of the procedure is demonstrated on examples of the Tanner
code and Margulis and codes (672 and 2640 bits long
respectively) operating over an Additive-White-Gaussian-Noise (AWGN) channel.Comment: 5 pages, 6 figure
Instanton analysis of Low-Density-Parity-Check codes in the error-floor regime
In this paper we develop instanton method introduced in [1], [2], [3] to
analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes
decoded iteratively in the so-called error-floor regime. We discuss statistical
properties of the numerical instanton-amoeba scheme focusing on detailed
analysis and comparison of two regular LDPC codes: Tanner's (155, 64, 20) and
Margulis' (672, 336, 16) codes. In the regime of moderate values of the
signal-to-noise ratio we critically compare results of the instanton-amoeba
evaluations against the standard Monte-Carlo calculations of the
Frame-Error-Rate.Comment: 5 pages, 5 figure
Rain initiation time in turbulent warm clouds
We present a mean-field model that describes droplet growth due to
condensation and collisions and droplet loss due to fallout. The model allows
for an effective numerical simulation. We study how the rain initiation time
depends on different parameters. We also present a simple model that allows one
to estimate the rain initiation time for turbulent clouds with an inhomogeneous
concentration of cloud condensation nuclei. In particular, we show that
over-seeding even a part of a cloud by small hygroscopic nuclei one can
substantially delay the onset of precipitation.Comment: submitted to Journal of Applied Meteorolog
Analysis of spatial correlations in a model 2D liquid through eigenvalues and eigenvectors of atomic level stress matrices
Considerations of local atomic level stresses associated with each atom
represent a particular approach to address structures of disordered materials
at the atomic level. We studied structural correlations in a two-dimensional
model liquid using molecular dynamics simulations in the following way. We
diagonalized the atomic level stress tensors of every atom and investigated
correlations between the eigenvalues and orientations of the eigenvectors of
different atoms as a function of distance between them. It is demonstrated that
the suggested approach can be used to characterize structural correlations in
disordered materials. In particular, we found that changes in the stress
correlation functions on decrease of temperature are the most pronounced for
the pairs of atoms with separation distance that corresponds to the first
minimum in the pair density function. We also show that the angular
dependencies of the stress correlation functions previously reported in [Phys.
Rev. E v.91, 032301 (2015)] related not to the alleged anisotropies of the
Eshelby's stress fields, but to the rotational properties of the stress
tensors.Comment: 14 pages, 9 figure
On higher order Codazzi tensors on complete Riemannian manifolds
We prove several Liouville-type non-existence theorems for higher order
Codazzi tensors and classical Codazzi tensors on complete and compact
Riemannian manifolds, in particular. These results will be obtained by using
theorems of the connections between the geometry of a complete smooth manifold
and the global behavior of its subharmonic functions. In conclusion, we show
applications of this method for global geometry of a complete locally
conformally flat Riemannian manifold with constant scalar curvature because its
Ricci tensor is a Codazzi tensor and for global geometry of a complete
hypersurface in a standard sphere because its second fundamental form is also a
Codazzi tensor
Predicting Failures in Power Grids: The Case of Static Overloads
Here we develop an approach to predict power grid weak points, and
specifically to efficiently identify the most probable failure modes in static
load distribution for a given power network. This approach is applied to two
examples: Guam's power system and also the IEEE RTS-96 system, both modeled
within the static Direct Current power flow model. Our algorithm is a power
network adaption of the worst configuration heuristics, originally developed to
study low probability events in physics and failures in error-correction. One
finding is that, if the normal operational mode of the grid is sufficiently
healthy, the failure modes, also called instantons, are sufficiently sparse,
i.e. the failures are caused by load fluctuations at only a few buses. The
technique is useful for discovering weak links which are saturated at the
instantons. It can also identify generators working at the capacity and
generators under capacity, thus providing predictive capability for improving
the reliability of any power network.Comment: 11 pages, 10 figure
Growth of density inhomogeneities in a flow of wave turbulence
We consider an advection of a passive scalar by a flow which is a
superposition of random waves. We find that such a flow can lead to an
exponential growth of the passive scalar fluctuations. We calculate the growth
rate at the fourth order in wave amplitudes and find it non-zero when either
both solenoidal and potential components are present in the flow or there are
potential waves with the same frequencies but different wavenumbers.Comment: 4 pages, 1 figur
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