Parameter and coupling estimation in small networks of Izhikevich's neurons.

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and temporally evolving networks. Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system.

How does a periodic rotating wave emerge from high-dimensional chaos in a ring of coupled chaotic oscillators?

A route to typical rotating waves from high-dimensional chaos is investigated in diffusively coupled chaotic Rössler oscillators. By increasing the coupling from zero, a high-dimensional spatiotemporal chaos changes into a coherent state, which is periodic in time and well ordered in space, through consecutive transitions. A crossover transition from spatially random chaos to spatially ordered chaos with phase locking and orientational equality (for two directions) breaking is a crucial step for establishing the typical spatial order of the rotating wave.

Partial synchronization and spontaneous spatial ordering in coupled chaotic systems.

A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some dynamical behaviors of these states are discussed both numerically and analytically.

Fractal properties of DNA walks.

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding parts.

Growth kinetics and morphology of a ballistic deposition model that incorporates surface diffusion for two species.

We introduce a ballistic deposition model for two kinds of particles (active and inactive) in (2+1) dimensions upon introducing surface diffusion for the inactive particles. A morphological structural transition is found as the probability of being the inactive particle increases. This transition is well defined by the change in the behavior of the surface width when it is plotted as a function of time and probability. The exponents alpha and beta calculated for different values of probability show the same behavior. The presence of both types of particles gives rise to three different processes that control the growing surface: overhanging, nonlocal growth, and diffusion. It finally leads to a morphological structural transition where the universality changes away from that of Kardar, Parisi, and Zhang, in (2+1) dimensions, but not into that of Edwards and Wilkinson.