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 $\tau = 2.06(2)$, followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to $N=2^{37}$ collapse perfectly onto a scaling curve characterized solely by the single exponent $\tau$. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as $N\rightarrow\infty$. 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