7,833 research outputs found
Symbolic Sequences and Tsallis Entropy
We address this work to investigate symbolic sequences with long-range
correlations by using computational simulation. We analyze sequences with two,
three and four symbols that could be repeated times, with the probability
distribution . For these sequences, we verified that
the usual entropy increases more slowly when the symbols are correlated and the
Tsallis entropy exhibits, for a suitable choice of , a linear behavior. We
also study the chain as a random walk-like process and observe a nonusual
diffusive behavior depending on the values of the parameter .Comment: Published in the Brazilian Journal of Physic
On the maximum bias functions of MM-estimates and constrained M-estimates of regression
We derive the maximum bias functions of the MM-estimates and the constrained
M-estimates or CM-estimates of regression and compare them to the maximum bias
functions of the S-estimates and the -estimates of regression. In these
comparisons, the CM-estimates tend to exhibit the most favorable
bias-robustness properties. Also, under the Gaussian model, it is shown how one
can construct a CM-estimate which has a smaller maximum bias function than a
given S-estimate, that is, the resulting CM-estimate dominates the S-estimate
in terms of maxbias and, at the same time, is considerably more efficient.Comment: Published at http://dx.doi.org/10.1214/009053606000000975 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos
Understanding of short-term synaptic depression (STSD) and other forms of
synaptic plasticity is a topical problem in neuroscience. Here we study the
role of STSD in the formation of complex patterns of brain rhythms. We use a
cortical circuit model of neural networks composed of irregular spiking
excitatory and inhibitory neurons having type 1 and 2 excitability and
stochastic dynamics. In the model, neurons form a sparsely connected network
and their spontaneous activity is driven by random spikes representing synaptic
noise. Using simulations and analytical calculations, we found that if the STSD
is absent, the neural network shows either asynchronous behavior or regular
network oscillations depending on the noise level. In networks with STSD,
changing parameters of synaptic plasticity and the noise level, we observed
transitions to complex patters of collective activity: mixed-mode and spindle
oscillations, bursts of collective activity, and chaotic behaviour.
Interestingly, these patterns are stable in a certain range of the parameters
and separated by critical boundaries. Thus, the parameters of synaptic
plasticity can play a role of control parameters or switchers between different
network states. However, changes of the parameters caused by a disease may lead
to dramatic impairment of ongoing neural activity. We analyze the chaotic
neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I.,
2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
Critical and resonance phenomena in neural networks
Brain rhythms contribute to every aspect of brain function. Here, we study
critical and resonance phenomena that precede the emergence of brain rhythms.
Using an analytical approach and simulations of a cortical circuit model of
neural networks with stochastic neurons in the presence of noise, we show that
spontaneous appearance of network oscillations occurs as a dynamical
(non-equilibrium) phase transition at a critical point determined by the noise
level, network structure, the balance between excitatory and inhibitory
neurons, and other parameters. We find that the relaxation time of neural
activity to a steady state, response to periodic stimuli at the frequency of
the oscillations, amplitude of damped oscillations, and stochastic fluctuations
of neural activity are dramatically increased when approaching the critical
point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
On the dynamics of bubbles in boiling water
We investigate the dynamics of many interacting bubbles in boiling water by
using a laser scattering experiment. Specifically, we analyze the temporal
variations of a laser intensity signal which passed through a sample of boiling
water. Our empirical results indicate that the return interval distribution of
the laser signal does not follow an exponential distribution; contrariwise, a
heavy-tailed distribution has been found. Additionally, we compare the
experimental results with those obtained from a minimalist phenomenological
model, finding a good agreement.Comment: Accepted for publication in Chaos, Solitons & Fractal
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