577 research outputs found
Replicating financial market dynamics with a simple self-organized critical lattice model
We explore a simple lattice field model intended to describe statistical
properties of high frequency financial markets. The model is relevant in the
cross-disciplinary area of econophysics. Its signature feature is the emergence
of a self-organized critical state. This implies scale invariance of the model,
without tuning parameters. Prominent results of our simulation are time series
of gains, prices, volatility, and gains frequency distributions, which all
compare favorably to features of historical market data. Applying a standard
GARCH(1,1) fit to the lattice model gives results that are almost
indistinguishable from historical NASDAQ data.Comment: 20 pages, 33 figure
Power spectrum of mass and activity fluctuations in a sandpile
We consider a directed abelian sandpile on a strip of size ,
driven by adding a grain randomly at the left boundary after every
time-steps. We establish the exact equivalence of the problem of mass
fluctuations in the steady state and the number of zeroes in the ternary-base
representation of the position of a random walker on a ring of size . We
find that while the fluctuations of mass have a power spectrum that varies as
for frequencies in the range , the activity
fluctuations in the same frequency range have a power spectrum that is linear
in .Comment: 8 pages, 10 figure
The origin of power-law distributions in self-organized criticality
The origin of power-law distributions in self-organized criticality is
investigated by treating the variation of the number of active sites in the
system as a stochastic process. An avalanche is then regarded as a first-return
random walk process in a one-dimensional lattice. Power law distributions of
the lifetime and spatial size are found when the random walk is unbiased with
equal probability to move in opposite directions. This shows that power-law
distributions in self-organized criticality may be caused by the balance of
competitive interactions. At the mean time, the mean spatial size for
avalanches with the same lifetime is found to increase in a power law with the
lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in
J. Phys.
Self-Organized Criticality model for Brain Plasticity
Networks of living neurons exhibit an avalanche mode of activity,
experimentally found in organotypic cultures. Here we present a model based on
self-organized criticality and taking into account brain plasticity, which is
able to reproduce the spectrum of electroencephalograms (EEG). The model
consists in an electrical network with threshold firing and activity-dependent
synapse strenghts. The system exhibits an avalanche activity power law
distributed. The analysis of the power spectra of the electrical signal
reproduces very robustly the power law behaviour with the exponent 0.8,
experimentally measured in EEG spectra. The same value of the exponent is found
on small-world lattices and for leaky neurons, indicating that universality
holds for a wide class of brain models.Comment: 4 pages, 3 figure
Plastic Flow, Voltage Bursts, and Vortex Avalanches in Superconductors
We use large-scale parallel simulations to compute the motion of
superconducting magnetic vortices during avalanches triggered by small field
increases. We find that experimentally observable voltage bursts correspond to
pulsing vortex movement along branched channels or winding chains, and relate
vortex flow images to features of statistical distributions. As pin density is
increased, a crossover occurs from interstitial motion in narrow easy-flow
winding channels with typical avalanche sizes, to pin-to-pin motion in broad
channels, characterized by a very broad distribution of sizes. Our results are
consistent with recent experiments.Comment: 4 pages, Latex, 4 figures included. Movies available at
http://www-personal.engin.umich.edu/~nor
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