Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Neuroimaging in anxiety disorders

Neuroimaging studies have gained increasing importance in validating neurobiological network hypotheses for anxiety disorders. Functional imaging procedures and radioligand binding studies in healthy subjects and in patients with anxiety disorders provide growing evidence of the existence of a complex anxiety network, including limbic, brainstem, temporal, and prefrontal cortical regions. Obviously, “normal anxiety” does not equal “pathological anxiety” although many phenomena are evident in healthy subjects, however to a lower extent. Differential effects of distinct brain regions and lateralization phenomena in different anxiety disorders are mentioned. An overview of neuroimaging investigations in anxiety disorders is given after a brief summary of results from healthy volunteers. Concluding implications for future research are made by the authors