Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent--to a large extent--from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a "conditional ERD," through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli.

We present a method for binary on-line classification of triggered but temporally blurred events that are embedded in noisy time series in the context of on-line discrimination between left and right imaginary hand-movement. In particular the goal of the binary classification problem is to obtain the decision, as fast and as reliably as possible from the recorded EEG single trials. To provide a probabilistic decision at every time-point t the presented method gathers information from two distinct sequences of features across time. In order to incorporate decisions from prior time-points we suggest an appropriate weighting scheme, that emphasizes time instances, providing a higher discriminatory power between the instantaneous class distributions of each feature, where the discriminatory power is quantified in terms of the Bayes error of misclassification. The effectiveness of this procedure is verified by its successful application in the 3rd BCI competition. Disclosure of the data after the competition revealed this approach to be superior with single trial error rates as low as 10.7, 11.5 and 16.7% for the three different sub jects under study.

We propose a novel method for the analysis of sequential data that exhibits an inherent mode switching. In particular, the data might be a non-stationary time series from a dynamical system that switches between multiple operating modes. Unlike other ap(cid:173) proaches, our method processes the data incrementally and without any training of internal parameters. We use an HMM with a dy(cid:173) namically changing number of states and an on-line variant of the Viterbi algorithm that performs an unsupervised segmentation and classification of the data on-the-fly, i.e. the method is able to pro(cid:173) cess incoming data in real-time. The main idea of the approach is to track and segment changes of the probability density of the data in a sliding window on the incoming data stream. The usefulness of the algorithm is demonstrated by an application to a switching dynamical system.