15,462 research outputs found
Sensitivity to initial conditions in self-organized critical systems
We discuss sensitivity to initial conditions in a model for avalanches in
granular media displaying self-organized criticality. We show that damage, due
to a small perturbation in initial conditions, does not spread. The damage
persists in a statistically time-invariant and scale-free form. We argue that
the origin of this behavior is the Abelian nature of the model, which
generalizes our results to all Abelian models, including the BTW model and the
Manna model. An ensemble average of the damage leads to seemingly time
dependent damage spreading. Scaling arguments show that this numerical result
is due to the time lag before avalanches reach the initial perturbation.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Bias-Correcting the Realized Range-Based Variance in the Presence of Market Microstructure Noise
Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to the rangestatistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise, and we can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it on high-frequency data from TAQ. We find that a bias-corrected range-statistic often has much smaller confidence intervals than the realized variance. --Bias-Correction,Integrated Variance,Market Microstructure Noise,Realized Range-Based Variance,Realized Variance
Myocardial Architecture and Patient Variability in Clinical Patterns of Atrial Fibrillation
Atrial fibrillation (AF) increases the risk of stroke by a factor of four to
five and is the most common abnormal heart rhythm. The progression of AF with
age, from short self-terminating episodes to persistence, varies between
individuals and is poorly understood. An inability to understand and predict
variation in AF progression has resulted in less patient-specific therapy.
Likewise, it has been a challenge to relate the microstructural features of
heart muscle tissue (myocardial architecture) with the emergent temporal
clinical patterns of AF. We use a simple model of activation wavefront
propagation on an anisotropic structure, mimicking heart muscle tissue, to show
how variation in AF behaviour arises naturally from microstructural differences
between individuals. We show that the stochastic nature of progressive
transversal uncoupling of muscle strands (e.g., due to fibrosis or gap
junctional remodelling), as occurs with age, results in variability in AF
episode onset time, frequency, duration, burden and progression between
individuals. This is consistent with clinical observations. The uncoupling of
muscle strands can cause critical architectural patterns in the myocardium.
These critical patterns anchor micro-re-entrant wavefronts and thereby trigger
AF. It is the number of local critical patterns of uncoupling as opposed to
global uncoupling that determines AF progression. This insight may eventually
lead to patient specific therapy when it becomes possible to observe the
cellular structure of a patient's heart.Comment: 5 pages, 4 figures. For supplementary materials please contact Kishan
A. Manani at [email protected]
Universality Class of One-Dimensional Directed Sandpile Models
A general n-state directed `sandpile' model is introduced. The stationary
properties of the n-state model are derived for n < infty, and analytical
arguments based on a central limit theorem show that the model belongs to the
universality class of the totally asymmetric Oslo model, with a crossover to
uncorrelated branching process behavior for small system sizes. Hence, the
central limit theorem allows us to identify the existence of a large
universality class of one-dimensional directed sandpile models.Comment: 4 pages, 2 figure
Continuity of the Explosive Percolation Transition
The explosive percolation problem on the complete graph is investigated via
extensive numerical simulations. We obtain the cluster-size distribution at the
moment when the cluster size heterogeneity becomes maximum. The distribution is
found to be well described by the power-law form with the decay exponent , followed by a hump. We then use the finite-size scaling method to
make all the distributions at various system sizes up to collapse
perfectly onto a scaling curve characterized solely by the single exponent
. We also observe that the instant of that collapse converges to a
well-defined percolation threshold from below as . Based on
these observations, we show that the explosive percolation transition in the
model should be continuous, contrary to the widely-spread belief of its
discontinuity.Comment: Some corrections during the revie
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