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We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential
A new synthesis of 9 alpha-hydroxy-alpha-agarofuran (6 alpha) is described, using a microbiological hydroxylation alpha-agarofuran (5) as the key reaction. The stereochemistry of the biohydroxylation was determined on the basis of a NOESY-experiment and GIAO calculations at the B3LYP/cc-pVDZ level. A strong gamma-effect was observed at C15 of the agarofuran ring which was correctly predicted by the GIAO-B3LYP calculations
In order to investigate the temporal characteristics of cognitive processing, we apply multivariate phase synchronization analysis to event-related potentials. The experimental design combines a semantic incongruity in a sentence context with a physical mismatch (color change). In the ERP average, these result in an N400 component and a P300-like positivity, respectively. Synchronization analysis shows an effect of global desynchronization in the theta band around 288 ms after stimulus presentation for the semantic incongruity, while the physical mismatch elicits an increase of global synchronization in the alpha band around 204 ms. Both of these effects clearly precede those in the ERP aver-age. Moreover, the delay between synchronization effect and ERP component correlates with the complexity Of the cognitive processes. (C) 2005 Lippincott Williams Wilkins