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

Transcranial duplex in the differential diagnosis of parkinsonian syndromes: a systematic review.

Item does not contain fulltextBACKGROUND: Transcranial duplex scanning (TCD) of the substantia nigra (SN) is increasingly used to diagnose Idiopathic Parkinson's Disease (IPD). Up until now 70 diagnostic studies have been published, not only on investigation of the SN, but also of the lenticular nucleus (LN) and the Raphe nuclei (RN). METHOD: We systematically reviewed all diagnostic TCD studies in parkinsonian patients up to June 2008. RESULTS: We found 35 eligible studies. Of the 1534 IPD patients investigated in the 35 studies 200 (13%) had an inconclusive SN-TCD. An increased echo-intensity of the SN was seen in 1167 (87%) of the 1334 IPD patients, 276 (12%) of the 2340 healthy controls and in 41 (30%) of the 138 patients with an atypical parkinsonian syndrome (APS). On the contrary, a pathological LNTCD was found more often in APS patients (79%) than in IPD patients (23%) and healthy controls (6%). A decreased echo-intensity of the RN was found more often in depressed (46%) than in non-depressed IPD patients (16%). CONCLUSIONS: SN-TCD accurately differentiates between patients with IPD and healthy controls, but not between patients with IPD and APS. LN-TCD is only moderate accurate to delineate IPD from APS, but combinations of SN- and LN-TCD may be more promising. RN-TCD has only marginal diagnostic accuracy in diagnosing depression in IPD and non-IPD patients. Before TCD can be implicated, more research is needed to standardize the TCD technique, to investigate the TCD in non-research settings and to determine the additional value of TCD compared with currently used clinical techniques like SPECT imaging

Frontiers of chaotic advection

We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, micro-fluidics, biological flows, and large-scale dispersion of pollutants in oceanographic and atmospheric flows