59 research outputs found
Asymmetrical dynamics of voltage spread in retinal horizontal cell networks
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Lateral voltage spread in electrically coupled retinal horizontal cell networks is the substrate of center-surround antagonism in bipolar and ganglion cells. We studied its spatial and temporal properties in more detail in turtle L1 horizontal cells by using a contrast border as light stimulus. Experimental data were contrasted with expectations from a linear continuum model to specify the impact of nonlinearities. The assumptions for the diffusion term of the continuum model were justified by neurobiotin labeling. Measured voltage spread revealed two different length constants Λ+ and Λ0, under illuminated and nonilluminated regions of the retina, respectively, as predicted by the linear model. Length constants in the illuminated region showed strong temporal dynamics. For the initial phase of the horizontal cell responses Λ+ was larger than Λo. This was also in accordance with the model. Right at the peak of the response, however, Λ+ dropped below Λo and did not change any more. It is this temporal reversal of asymmetry in voltage spread and not the decrease of Λ+ itself that is lacked by the linear model. The observed independence of the mean ratio Λ+/Λo from light intensity in both the peak and the plateau phases of horizontal cell responses contradicts the linear assumption, too. These two effects have to be addressed to local nonlinearities in the horizontal cell network like a negative feedback loop from photoreceptors and/or voltage-dependent conductances. Due to the failure of the linear model, firm conclusions about the membrane resistance and the coupling resistance of the horizontal cell network cannot be drawn from length constant measurements.Peer Reviewe
Metastability for reversible probabilistic cellular automata with self--interaction
The problem of metastability for a stochastic dynamics with a parallel
updating rule is addressed in the Freidlin--Wentzel regime, namely, finite
volume, small magnetic field, and small temperature. The model is characterized
by the existence of many fixed points and cyclic pairs of the zero temperature
dynamics, in which the system can be trapped in its way to the stable phase.
%The characterization of the metastable behavior %of a system in the context of
parallel dynamics is a very difficult task, %since all the jumps in the
configuration space are allowed. Our strategy is based on recent powerful
approaches, not needing a complete description of the fixed points of the
dynamics, but relying on few model dependent results. We compute the exit time,
in the sense of logarithmic equivalence, and characterize the critical droplet
that is necessarily visited by the system during its excursion from the
metastable to the stable state. We need to supply two model dependent inputs:
(1) the communication energy, that is the minimal energy barrier that the
system must overcome to reach the stable state starting from the metastable
one; (2) a recurrence property stating that for any configuration different
from the metastable state there exists a path, starting from such a
configuration and reaching a lower energy state, such that its maximal energy
is lower than the communication energy
Magnetic order in the Ising model with parallel dynamics
It is discussed how the equilibrium properties of the Ising model are
described by an Hamiltonian with an antiferromagnetic low temperature behavior
if only an heat bath dynamics, with the characteristics of a Probabilistic
Cellular Automaton, is assumed to determine the temporal evolution of the
system.Comment: 9 pages, 3 figure
An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions
We solve exactly a special case of the anisotropic directed bond percolation
problem in three dimensions, in which the occupation probability is 1 along two
spatial directions, by mapping it to a five-vertex model. We determine the
asymptotic shape of the ininite cluster and hence the direction dependent
critical probability. The exponents characterising the fluctuations of the
boundary of the wetted cluster in d-dimensions are related to those of the
(d-2)-dimensional KPZ equation.Comment: 4 pages, RevTex, 4 figures. 1 reference added, minor change
The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes
A variation of Gallager error-correcting codes is investigated using
statistical mechanics. In codes of this type, a given message is encoded into a
codeword which comprises Boolean sums of message bits selected by two randomly
constructed sparse matrices. The similarity of these codes to Ising spin
systems with random interaction makes it possible to assess their typical
performance by analytical methods developed in the study of disordered systems.
The typical case solutions obtained via the replica method are consistent with
those obtained in simulations using belief propagation (BP) decoding. We
discuss the practical implications of the results obtained and suggest a
computationally efficient construction for one of the more practical
configurations.Comment: 35 pages, 4 figure
Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase
We study the short-time dynamics of systems that develop ``quasi long-range
order'' after a quench to the Kosterlitz-Thouless phase. With the working
hypothesis that the ``universal short-time behavior'', previously found in
Ising-like systems, also occurs in the Kosterlitz-Thouless phase, we explore
the scaling behavior of thermodynamic variables during the relaxational process
following the quench. As a concrete example, we investigate the two-dimensional
-state clock model by Monte Carlo simulation. The exponents governing the
magnetization, the second moment, and the autocorrelation function are
calculated. From them, by means of scaling relations, estimates for the
equilibrium exponents and are derived. In particular, our estimates
for the temperature-dependent anomalous dimension that governs the
static correlation function are consistent with existing analytical and
numerical results and, thus, confirm our working hypothesis.Comment: 16 pages, 9 postscript figures, REVTEX 3.0, submitted to Phys. Rev.
Critical droplets in Metastable States of Probabilistic Cellular Automata
We consider the problem of metastability in a probabilistic cellular
automaton (PCA) with a parallel updating rule which is reversible with respect
to a Gibbs measure. The dynamical rules contain two parameters and
which resemble, but are not identical to, the inverse temperature and external
magnetic field in a ferromagnetic Ising model; in particular, the phase diagram
of the system has two stable phases when is large enough and is
zero, and a unique phase when is nonzero. When the system evolves, at small
positive values of , from an initial state with all spins down, the PCA
dynamics give rise to a transition from a metastable to a stable phase when a
droplet of the favored phase inside the metastable phase reaches a
critical size. We give heuristic arguments to estimate the critical size in the
limit of zero ``temperature'' (), as well as estimates of the
time required for the formation of such a droplet in a finite system. Monte
Carlo simulations give results in good agreement with the theoretical
predictions.Comment: 5 LaTeX picture
Tighter decoding reliability bound for Gallager's error-correcting code
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored
Arrangements of human telomere DNA quadruplex in physiologically relevant K+ solutions
The arrangement of the human telomeric quadruplex in physiologically relevant conditions has not yet been unambiguously determined. Our spectroscopic results suggest that the core quadruplex sequence G3(TTAG3)3 forms an antiparallel quadruplex of the same basket type in solution containing either K+ or Na+ ions. Analogous sequences extended by flanking nucleotides form a mixture of the antiparallel and hybrid (3 + 1) quadruplexes in K+-containing solutions. We, however, show that long telomeric DNA behaves in the same way as the basic G3(TTAG3)3 motif. Both G3(TTAG3)3 and long telomeric DNA are also able to adopt the (3 + 1) quadruplex structure: Molecular crowding conditions, simulated here by ethanol, induced a slow transition of the K+-stabilized quadruplex into the hybrid quadruplex structure and then into a parallel quadruplex arrangement at increased temperatures. Most importantly, we demonstrate that the same transitions can be induced even in aqueous, K+-containing solution by increasing the DNA concentration. This is why distinct quadruplex structures were detected for AG3(TTAG3)3 by X-ray, nuclear magnetic resonance and circular dichrosim spectroscopy: Depending on DNA concentration, the human telomeric DNA can adopt the antiparallel quadruplex, the (3 + 1) structure, or the parallel quadruplex in physiologically relevant concentrations of K+ ions
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