608 research outputs found
Modeling Interaction of Fluid and Salt in an Aquifer/Lagoon System
Auther Posting. ©The Authers 2009 The full text of this article is published in GROUND WATER, 47, 1, 35-48. It is available online from Blackwell-Synergy at https://doi.org/10.1111/j.1745-6584.2008.00482.xArticleGROUND WATER. 47(1):35-48 (2009)journal articl
Critical Noise Levels for LDPC decoding
We determine the critical noise level for decoding low density parity check
error correcting codes based on the magnetization enumerator (\cM), rather
than on the weight enumerator (\cW) employed in the information theory
literature. The interpretation of our method is appealingly simple, and the
relation between the different decoding schemes such as typical pairs decoding,
MAP, and finite temperature decoding (MPM) becomes clear. In addition, our
analysis provides an explanation for the difference in performance between MN
and Gallager codes. Our results are more optimistic than those derived via the
methods of information theory and are in excellent agreement with recent
results from another statistical physics approach.Comment: 9 pages, 5 figure
Extended Ensemble Monte Carlo
``Extended Ensemble Monte Carlo''is a generic term that indicates a set of
algorithms which are now popular in a variety of fields in physics and
statistical information processing. Exchange Monte Carlo (Metropolis-Coupled
Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte
Carlo), and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical
members of this family. Here we give a cross-disciplinary survey of these
algorithms with special emphasis on the great flexibility of the underlying
idea. In Sec.2, we discuss the background of Extended Ensemble Monte Carlo. In
Sec.3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo,
Simulated Tempering, Multicanonical Monte Carlo are introduced. In Sec.6, we
give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang.
Strategies for the construction of special-purpose extended ensembles are
discussed in Sec.7. We stress that an extension is not necessary restricted to
the space of energy or temperature. Even unphysical (unrealizable)
configurations can be included in the ensemble, if the resultant fast mixing of
the Markov chain offsets the increasing cost of the sampling procedure.
Multivariate (multi-component) extensions are also useful in many examples. In
Sec.8, we give a survey on extended ensembles with a state space whose
dimensionality is dynamically varying. In the appendix, we discuss advantages
and disadvantages of three types of extended ensemble algorithms.Comment: Major revision that includes addition of concrete examples,
references, improved introduction to Multicanonical MC, change in the order
of the sections, and a number of small but important corrections. 49 pages,
no figure
Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble
A novel family of dynamical Monte Carlo algorithms for lattice polymers is
proposed. Our central idea is to simulate an extended ensemble in which the
self-avoiding condition is systematically weakened. The degree of the
self-overlap is controlled in a similar manner as the multicanonical ensemble.
As a consequence, the ensemble --the multi-self-overlap ensemble-- contains
adequate portions of self-overlapping conformations as well as higher energy
ones. It is shown that the multi-self-overlap ensemble algorithm reproduce
correctly the canonical averages at finite temperatures of the HP model of
lattice proteins. Moreover, it outperforms massively a standard multicanonical
algorithm for a difficult example of a polymer with 8-stickers. Alternative
algorithm based on exchange Monte Carlo method is also discussed.Comment: 5 Pages, 4 Postscript figures, uses epsf.st
Analysis of common attacks in LDPCC-based public-key cryptosystems
We analyze the security and reliability of a recently proposed class of
public-key cryptosystems against attacks by unauthorized parties who have
acquired partial knowledge of one or more of the private key components and/or
of the plaintext. Phase diagrams are presented, showing critical partial
knowledge levels required for unauthorized decryptionComment: 14 pages, 6 figure
Testing Error Correcting Codes by Multicanonical Sampling of Rare Events
The idea of rare event sampling is applied to the estimation of the
performance of error-correcting codes. The essence of the idea is importance
sampling of the pattern of noises in the channel by Multicanonical Monte Carlo,
which enables efficient estimation of tails of the distribution of bit error
rate. The idea is successfully tested with a convolutional code
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes
We investigate the use of Gallager's low-density parity-check (LDPC) codes in
a broadcast channel, one of the fundamental models in network information
theory. Combining linear codes is a standard technique in practical network
communication schemes and is known to provide better performance than simple
timesharing methods when algebraic codes are used. The statistical physics
based analysis shows that the practical performance of the suggested method,
achieved by employing the belief propagation algorithm, is superior to that of
LDPC based timesharing codes while the best performance, when received
transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
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