223 research outputs found
Scaling behaviour in probabilistic neuronal cellular automata
We study a neural network model of interacting stochastic discrete two--state
cellular automata on a regular lattice. The system is externally tuned to a
critical point which varies with the degree of stochasticity (or the effective
temperature). There are avalanches of neuronal activity, namely spatially and
temporally contiguous sites of activity; a detailed numerical study of these
activity avalanches is presented, and single, joint and marginal probability
distributions are computed. At the critical point, we find that the scaling
exponents for the variables are in good agreement with a mean--field theory.Comment: 7 pages, 4 figures Accepted for publication in Physical Review
Memoryless nonlinear response: A simple mechanism for the 1/f noise
Discovering the mechanism underlying the ubiquity of noise
has been a long--standing problem. The wide range of systems in which the
fluctuations show the implied long--time correlations suggests the existence of
some simple and general mechanism that is independent of the details of any
specific system. We argue here that a {\it memoryless nonlinear response}
suffices to explain the observed non--trivial values of : a random
input noisy signal with a power spectrum varying as ,
when fed to an element with such a response function gives an output
that can have a power spectrum with . As an illustrative example, we show that an input Brownian noise
() acting on a device with a sigmoidal response function R(S)=
\sgn(S)|S|^x, with , produces an output with , for . Our discussion is easily extended to more general types of
input noise as well as more general response functions.Comment: 5 pages, 5 figure
The Scattering amplitude for Rationally extended shape invariant Eckart potentials
We consider the rationally extended exactly solvable Eckart potentials which
exhibit extended shape invariance property. These potentials are isospectral to
the conventional Eckart potential. The scattering amplitude for these
rationally ex- tended potentials is calculated analytically for the generalized
mth (m = 1, 2, 3, ...) case by considering the asymptotic behavior of the
scattering state wave functions which are written in terms of some new
polynomials related to the Jacobi polyno- mials. As expected, in the m = 0
limit, this scattering amplitude goes over to the scattering amplitude for the
conventional Eckart potential.Comment: 8 pages. Latex, No fi
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