Type of self-organized criticality model based on neural networks

Epileptic seizures: Quakes of the brain?

A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event) is shown to exist between two classes of seizures ("focal" in humans and generalized in animals) and earthquakes. Increments in excitatory interneuronal coupling in animals expose the system's dependence on this parameter and its dynamical transmutability: moderate increases lead to power-law behavior of seizure energy and interevent times, while marked ones to scale-free (power-law) coextensive with characteristic scales and events. The coextensivity of power law and characteristic size regimes is predicted by models of coupled heterogeneous threshold oscillators of relaxation and underscores the role of coupling strength in shaping the dynamics of these systems.

Optimization via Intermittency with a Self-Organizing Neural Network

One of the major obstacles in using neural networks to solve combinatorial optimization problems is the convergence toward one of the many local minima instead of the global minima. In this letter, we propose a technique that enables a self-organizing neural network to escape from local minima by virtue of the intermittency phenomenon. It gives rise to novel search dynamics that allow the system to visit multiple global minima as meta-stable states. Numerical experiments performed suggest that the phenomenon is a combined effect of Kohonen-type competitive learning and the iterated softmax function operating near bifurcation. The resultant intermittent search exhibits fractal characteristics when the optimization performance is at its peak in the form of 1/f signals in the time evolution of the cost, as well as power law distributions in the meta-stable solution states. The N-Queens problem is used as an example to illustrate the meta-stable convergence process that sequentially generates, in a single run, 92 solutions to the 8-Queens problem and 4024 solutions to the 17-Queens problem.

Rapid self-organized criticality: Fractal evolution in extreme environments

We introduce the phenomenon of rapid self-organized criticality (RSOC) and show that, like some models of self-organized criticality (SOC), RSOC generates scale-invariant event distributions and 1/f noise. Unlike SOC, however, RSOC persists despite more than an order of magnitude variation in driving rate and displays extremely thick and dynamic branching geometry. Starting with an initial set of parameter values, we perform two numerical experiments in which nonequilibrium RSOC systems are tuned towards their critical points. The approach to the critical state is tracked using average branching rates, which must equal 1 if systems are genuinely critical.