3,705 research outputs found
Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
We obtain phase diagrams of regular and irregular finite connectivity
spin-glasses. Contact is firstly established between properties of the phase
diagram and the performances of low density parity check codes (LDPC) within
the Replica Symmetric (RS) ansatz. We then study the location of the dynamical
and critical transition of these systems within the one step Replica Symmetry
Breaking theory (RSB), extending similar calculations that have been performed
in the past for the Bethe spin-glass problem. We observe that, away from the
Nishimori line, in the low temperature region, the location of the dynamical
transition line does change within the RSB theory, in comparison with the (RS)
case. For LDPC decoding over the binary erasure channel we find, at zero
temperature and rate R=1/4 an RS critical transition point located at p_c =
0.67 while the critical RSB transition point is located at p_c = 0.7450, to be
compared with the corresponding Shannon bound 1-R. For the binary symmetric
channel (BSC) we show that the low temperature reentrant behavior of the
dynamical transition line, observed within the RS ansatz, changes within the
RSB theory; the location of the dynamical transition point occurring at higher
values of the channel noise. Possible practical implications to improve the
performances of the state-of-the-art error correcting codes are discussed.Comment: 21 pages, 15 figure
Solitary coherent structures in viscoelastic shear flow: computation and mechanism
Starting from stationary bifurcations in Couette-Dean flow, we compute
nontrivial stationary solutions in inertialess viscoelastic circular Couette
flow. These solutions are strongly localized vortex pairs, exist at arbitrarily
large wavelengths, and show hysteresis in the Weissenberg number, similar to
experimentally observed ``diwhirl'' patterns. Based on the computed velocity
and stress fields, we elucidate a heuristic, fully nonlinear mechanism for
these flows. We propose that these localized, fully nonlinear structures
comprise fundamental building blocks for complex spatiotemporal dynamics in the
flow of elastic liquids.Comment: 5 pages text and 4 figures. Submitted to Physical Review Letter
Effective-mass Klein-Gordon Equation for non-PT/non-Hermitian Generalized Morse Potential
The one-dimensional effective-mass Klein-Gordon equation for the real, and
non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved
by taking a series expansion for the wave function. The energy eigenvalues, and
the corresponding eigenfunctions are obtained. They are also calculated for the
constant mass case.Comment: 14 page
Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
The spectrum of the non-hermitian asymmetric XXZ-chain with additional
non-diagonal boundary terms is studied. The lowest lying eigenvalues are
determined numerically. For the ferromagnetic and completely asymmetric chain
that corresponds to a reaction-diffusion model with input and outflow of
particles the smallest energy gap which corresponds directly to the inverse of
the temporal correlation length shows the same properties as the spatial
correlation length of the stationary state. For the antiferromagnetic chain
with both boundary terms, we find a conformal invariant spectrum where the
partition function corresponds to the one of a Coulomb gas with only magnetic
charges shifted by a purely imaginary and a lattice-length dependent constant.
Similar results are obtained by studying a toy model that can be diagonalized
analytically in terms of free fermions.Comment: LaTeX, 26 pages, 1 figure, uses ioplppt.st
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
Clinical and hospitalisation predictors of COVID-19 in the first month of the pandemic, Portugal
COVID-19 mainly presents as a respiratory disease with flu-like symptoms, however, recent findings suggest that non-respiratory symptoms can occur early in the infection and cluster together in different groups in different regions. We collected surveillance data among COVID-19 suspected cases tested in mainland Portugal during the first wave of the pandemic, March-April 2020. A multivariable logistic-regression analysis was performed to ascertain the effects of age, sex, prior medical condition and symptoms on the likelihood of testing positive and hospitalisation. Of 25,926 COVID-19 suspected cases included in this study, 5,298 (20%) tested positive. Symptoms were grouped into ten clusters, of which two main ones: one with cough and fever and another with the remainder. There was a higher odds of a positive test with increasing age, myalgia and headache. The odds of being hospitalised increased with age, presence of fever, dyspnoea, or having a prior medical condition although these results varied by region. Presence of cough and other respiratory symptoms did not predict COVID-19 compared to non-COVID respiratory disease patients in any region. Dyspnoea was a strong determinant of hospitalisation, as well as fever and the presence of a prior medical condition, whereas these results varied by region.The author(s) received no specific funding for this work
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
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
We present a new approximation scheme for the centrifugal term to obtain a
quasi-exact analytical bound state solutions within the framework of the
position-dependent effective mass radial Klein-Gordon equation with the scalar
and vector Hulth\'{e}n potentials in any arbitrary dimension and orbital
angular momentum quantum numbers The Nikiforov-Uvarov (NU) method is used
in the calculations. The relativistic real energy levels and corresponding
eigenfunctions for the bound states with different screening parameters have
been given in a closed form. It is found that the solutions in the case of
constant mass and in the case of s-wave () are identical with the ones
obtained in literature.Comment: 25 pages, 1 figur
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