5,869 research outputs found
Replica Symmetry Breaking in Attractor Neural Network Models
The phenomenon of replica symmetry breaking is investigated for the retrieval
phases of Hopfield-type network models. The basic calculation is done for the
generalized version of the standard model introduced by Horner [1] and by
Perez-Vicente and Amit [2] which can exhibit low mean levels of neural
activity. For a mean activity the Hopfield model is recovered. In
this case, surprisingly enough, we cannot confirm the well known one step
replica symmetry breaking (1RSB) result for the storage capacity which was
presented by Crisanti, Amit and Gutfreund [3] (\alpha_c^{\hbox{\mf
1RSB}}\simeq 0.144). Rather, we find that 1RSB- and 2RSB-Ans\"atze yield only
slightly increased capacities as compared to the replica symmetric value
(\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.138\,186 and \alpha_c^{\hbox{\mf
2RSB}}\simeq 0.138\,187 compared to \alpha_c^{\hbox{\mf RS}}\simeq
0.137\,905), significantly smaller also than the value \alpha_c^{\hbox{\mf
sim}} = 0.145\pm 0.009 reported from simulation studies. These values still
lie within the recently discovered reentrant phase [4]. We conjecture that in
the infinite Parisi-scheme the reentrant behaviour disappears as is the case in
the SK-spin-glass model (Parisi--Toulouse-hypothesis). The same qualitative
results are obtained in the low activity range.Comment: Latex file, 20 pages, 8 Figures available from the authors upon
request, HD-TVP-94-
Typical performance of low-density parity-check codes over general symmetric channels
Typical performance of low-density parity-check (LDPC) codes over a general
binary-input output-symmetric memoryless channel is investigated using methods
of statistical mechanics. Theoretical framework for dealing with general
symmetric channels is provided, based on which Gallager and MacKay-Neal codes
are studied as examples of LDPC codes. It has been shown that the basic
properties of these codes known for particular channels, including the property
to potentially saturate Shannon's limit, hold for general symmetric channels.
The binary-input additive-white-Gaussian-noise channel and the binary-input
Laplace channel are considered as specific channel noise models.Comment: 10 pages, 4 figures, RevTeX4; an error in reference correcte
Spectral density of random graphs with topological constraints
The spectral density of random graphs with topological constraints is
analysed using the replica method. We consider graph ensembles featuring
generalised degree-degree correlations, as well as those with a community
structure. In each case an exact solution is found for the spectral density in
the form of consistency equations depending on the statistical properties of
the graph ensemble in question. We highlight the effect of these topological
constraints on the resulting spectral density.Comment: 24 pages, 6 figure
Dynamical Induction of s-wave Component in d-wave Superconductor Driven by Thermal Fluctuations
We investigated the mutual induction effects between the d-wave and the
s-wave components of order parameters due to superconducting fluctuation above
the critical temperatures and calculated its contributions to paraconductivity
and excess Hall conductivity based on the two-component stochastic TDGL
equation. It is shown that the coupling of two components increases
paraconductivity while it decreases excess Hall conductivity compared to the
cases when each component fluctuates independently. We also found the singular
behavior in the paraconductivity and the excess Hall conductivity dependence on
the coupling parameter which is consistent with the natural restriction among
the coefficients of gradient terms.Comment: 10 pages, 4 figures included, submitted to J.Phys.Soc.Jp
Statistical Physics of Irregular Low-Density Parity-Check Codes
Low-density parity-check codes with irregular constructions have been
recently shown to outperform the most advanced error-correcting codes to date.
In this paper we apply methods of statistical physics to study the typical
properties of simple irregular codes.
We use the replica method to find a phase transition which coincides with
Shannon's coding bound when appropriate parameters are chosen.
The decoding by belief propagation is also studied using statistical physics
arguments; the theoretical solutions obtained are in good agreement with
simulations. We compare the performance of irregular with that of regular codes
and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP
Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels
Using analytical methods of statistical mechanics, we analyse the typical
behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with
binary inputs under LDPC network coding and joint decoding. The saddle point
equations for the replica symmetric solution are found in particular
realizations of this channel, including a small and large number of
transmitters and receivers. In particular, we examine the cases of a single
transmitter, a single receiver and the symmetric and asymmetric interference
channels. Both dynamical and thermodynamical transitions from the ferromagnetic
solution of perfect decoding to a non-ferromagnetic solution are identified for
the cases considered, marking the practical and theoretical limits of the
system under the current coding scheme. Numerical results are provided, showing
the typical level of improvement/deterioration achieved with respect to the
single transmitter/receiver result, for the various cases.Comment: 25 pages, 7 figure
New bounds on trilinear R-parity violation from lepton flavor violating observables
Many extensions of the leptonic sector of the Minimal Supersymmetric Standard
Model (MSSM) are known, most of them leading to observable flavor violating
effects. It has been recently shown that the 1-loop contributions to lepton
flavor violating three-body decays involving the boson
may be dominant, that is, much more important than the usual photonic penguins.
Other processes like - conversion in nuclei and flavor violating
decays into mesons are also enhanced by the same effect. This is for instance
also the case in the MSSM with trilinear R-parity violation. The aim of this
work is to derive new bounds on the relevant combinations of R-parity violating
couplings and to compare them with previous results in the literature. For
heavy supersymmetric spectra the limits are improved by several orders of
magnitude. For completeness, also constraints coming from flavor violating
-decays and tree-level decay channels are presented
for a set of benchmark points.Comment: 21 pages; 5 figures; v2: corrected bug, conclusion unchange
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