Multiscale dynamics and robust critical scaling in a continuum current sheet model.

We analyze the self-organized critical behavior of a continuum running avalanche model. We demonstrate that over local interaction scales, the model behavior is affected by low-dimensional chaotic dynamics that plays the role of the primary noise source. With the help of scale-free avalanches, the uncertainty associated with chaos is distributed over a variety of intermediate scales and thus gives rise to spatiotemporal fluctuations that are characterized by power-law distribution functions. We show that globally, the continuum model displays structurally stable critical scaling that can be observed in a finite region in the control parameter space. In this region, the system exhibits a power-law critical divergence of the integrated response function over a broad range of dissipation rates. The observed behavior involves a remarkably stable spatial configuration. We explain the robust features of the model by the adjustable dynamics of its global loading-unloading cycle, which allows maintaining the long-term stationary state without affecting the intrinsic avalanche dynamics.

Modeling substorm dynamics of the magnetosphere: from self-organization and self-organized criticality to nonequilibrium phase transitions.

Earth's magnetosphere during substorms exhibits a number of characteristic features such as the signatures of low effective dimension, hysteresis, and power-law spectra of fluctuations on different scales. The largest substorm phenomena are in reasonable agreement with low-dimensional magnetospheric models and in particular those of inverse bifurcation. However, deviations from the low-dimensional picture are also quite considerable, making the nonequilibrium phase transition more appropriate as a dynamical analog of the substorm activity. On the other hand, the multiscale magnetospheric dynamics cannot be limited to the features of self-organized criticality (SOC), which is based on a class of mathematical analogs of sandpiles. Like real sandpiles, during substorms the magnetosphere demonstrates features, that are distinct from SOC and are closer to those of conventional phase transitions. While the multiscale substorm activity resembles second-order phase transitions, the largest substorm avalanches are shown to reveal the features of first-order nonequilibrium transitions including hysteresis phenomena and a global structure of the type of a temperature-pressure-density diagram. Moreover, this diagram allows one to find a critical exponent, that reflects the multiscale aspect of the substorm activity, different from the power-law frequency and scale spectra of autonomous systems, although quite consistent with second-order phase transitions. In contrast to SOC exponents, this exponent relates input and output parameters of the magnetosphere. Using an analogy to the dynamical Ising model in the mean-field approximation, we show the connection between the data-derived exponent of nonequilibrium transitions in the magnetosphere and the standard critical exponent beta of equilibrium second-order phase transitions.

The potential of statistical state space models in urban ozone forecasting.

State space models for tropospheric urban ozone prediction are introduced and compared with linear regression models. The linear and non-linear state space models make accurate short-term predictions of the ozone dynamics. The average prediction error one hour in advance is 7 microg/m(3) and increases logarithmically with time until it reaches 26 microg/m(3) after 30 days. For a given sequence of solar radiation inputs, predictions converge exponentially with a time scale of 8 hours, so that the model is insensitive to perturbations of more than 150 microg/m(3) O(3). The slow increase of the prediction error in addition to the uniqueness of the prediction are encouraging for applications of state space models in forecasting ozone levels when coupled with a model that predicts total radiation. Since a radiation prediction model will be more accurate during cloud-free conditions, in addition to the fact that the state space models perform better during the summer months, state space models are suitable for applications in sunny environments.

The EEG spectra of Alzheimer's disease.

Sixteen Alzheimer's and 16 non-Alzheimer's dementia patients, the two groups being matched for dementia, as well as 10 normal controls were given an EEG examination with 12 monopolar leads during an awake-resting condition. Power spectra (16 s) were obtained in 12 brain areas for 18 frequency bands (0-36 Hz). An 11-point dementia scale furnished the dementia scores. Analyses of variance were performed. Data confirmed earlier findings of an increase in slow activity and a decrease in fast activity for the demented groups. It further demonstrated that these EEG features were not related to dementia per se since the Alzheimer's group (matched for dementia) exhibited a spectral curve having a maximum at 1 Hz and an exponential asymptotic power characterized by decreasing power with increasing frequency without additional features or remnant of dominant activity. The study demonstrated that the decrease in frequency of alpha activity is perhaps more significant in identifying dementia of the non-Alzheimer type even though this characteristic may be present in the earlier stages of Alzheimer's dementia. It is hypothesized that the characteristics shown by the Alzheimer's group may be related to the presence of neurofibrillary tangles and plaques which are more prevalent in Alzheimer's patients.