Besov regularity of solutions to the p-Poisson equation

In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau = \sigma/d+1/p$, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear approximation methods. It turns out that, especially for solutions to $p$-Poisson equations with homogeneous Dirichlet boundary conditions on bounded polygonal domains, the Besov regularity is significantly higher than the Sobolev regularity which justifies the use of adaptive algorithms. This type of results is obtained by combining local H\"older with global Sobolev estimates. In particular, we prove that intersections of locally weighted H\"older spaces and Sobolev spaces can be continuously embedded into the specific scale of Besov spaces we are interested in. The proof of this embedding result is based on wavelet characterizations of Besov spaces.Comment: 45 pages, 2 figure

Platelet adhesion onto immobilized fibrinogen under arterial and venous in-vitro flow conditions does not significantly differ between men and women

BACKGROUND: Gender-related differences in incidence of arterial thrombosis have been a focus of interest for years. The platelet integrin αIIbβ3 is primarily responsible for the interaction between platelets and fibrinogen and consecutive thrombus growth. In this study, we evaluated platelet adhesion onto immobilized fibrinogen under venous and arterial flow conditions in men and women. METHODS: Platelets in whole anticoagulated blood were labelled with the fluorescence dye Mepacrine and perfused through the rectangular flow chamber over glass cover slips coated with fibrinogen (shear rates of 50 s(-1), 500 s(-1 )and 1500 s(-1)). A fluorescence laser-scan microscope was used for visualisation and quantification of platelet adhesion at 15 seconds, 1 and 5 minutes after the start of perfusion. RESULTS: During perfusion, the platelet adhesion linearly increased in regard to exposition time and shear rate. After five minutes of perfusion the platelet adhesion onto immobilized fibrinogen showed no significant gender related difference, neither at 50 s(-1 )nor at 500 s(-1 )and 1500 s(-1 )(p > 0.05), respectively. No significant difference in platelet adhesion onto immobilized fibrinogen, in regard to the menopausal status, was either observed (p > 0.05). CONCLUSION: In our in vitro experimental system, hormonal differences between men and women did not influence platelet adhesion onto immobilized fibrinogen, neither under venous nor under arterial rheological conditions

Effects of AV delay programming on ventricular resynchronisation: role of radionuclide ventriculography

Purpose: Optimal atrioventricular delay (AVD) setting for cardiac resynchronisation therapy, i.e. biventricular pacing in patients with heart failure, remains a formidable challenge. Thus, the purpose of this study was to evaluate the effects of different AVD on inter- and intra-ventricular resynchronisation using phase histograms of radionuclide ventriculography (RNV). Methods: In 17 consecutive patients (mean age 64 ± 6years), RNV was performed 236 ± 350days after pacemaker implantation for cardiac resynchronisation therapy. Images were acquired during atrial pacing at 80bpm and during biventricular pacing with AVD ranging from 80 to 160ms. Inter-ventricular dyssynchrony was measured by the delay between the mean phase angles of the left and right ventricles. Intra-ventricular dyssynchrony was measured by the standard deviation (SD) of left ventricular phase histograms. Results: Left ventricular (LV) ejection fraction (EF) was inversely correlated to LV dyssynchrony (SD of LV phase histogram, R = −0.82, p < 0.0001). However, the increase in LVEF by biventricular pacing (mean +4.4 ± 4%) showed only modest correlation to the resulting resynchronisation effect (characterised by a −13 ± 8° decrease in LV phase histogram SD, R = −0.38, p < 0.0001). Conclusion: RNV is helpful in optimising pacing parameters for resynchronisation therapy. Varying AVD did not have a major impact on intra- or inter-ventricular resynchronisation. Thus, the benefit of AVD-based LVEF optimisation seems to result from atrioventricular resynchronisatio

Pulmonary Vein Isolation for Vagotonic, Adrenergic, and Random Episodes of Paroxysmal Atrial Fibrillation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75410/1/j.1540-8167.2004.03432.x.pd

Evolution of Neuropsychological Deficits in First-Ever Isolated Ischemic Thalamic Stroke and Their Association With Stroke Topography: A Case-Control Study.

BACKGROUND The thalamus plays an essential role in cognition. Cognitive deficits have to date mostly been studied retrospectively in chronic thalamic stroke in small cohorts. Studies prospectively evaluating the evolution of cognitive deficits and their association with thalamic stroke topography are lacking. This knowledge is relevant for targeted patient diagnostics and rehabilitation. METHODS Thirty-seven patients (57.5±17.5 [mean±SD] years, 57% men) with first-ever acute isolated ischemic stroke covering the anterior (n=5), paramedian (n=12), or inferolateral (n=20) thalamus and 37 in-patient controls without stroke with similar vascular risk factors matched for age and sex were prospectively studied. Cognition was evaluated using predefined tests at 1, 6, 12, and 24 months. Voxel-based lesion-symptom mapping was used to determine associations between neuropsychological deficits and stroke topography. RESULTS Patients with anterior thalamic stroke revealed severe deficits in verbal memory (median T score [Q1-Q3]: 39.1 [36.1-44.1]), language (31.8 [31.0-43.8]), and executive functions (43.8 [35.5-48.1]) at 1 month compared with controls (verbal memory: 48.5 [43.6-61.0], language: 55.7 [42.3-61.1], executive functions: 51.3 [50.1-56.8]). Patients with paramedian thalamic stroke showed moderate language (44.7 [42.8-55.9]) and executive (49.5 [44.3-55.1]) deficits and no verbal memory deficits (48.1 [42.5-54.7]) at 1 month compared with controls (59.0 [47.0-64.5]; 59.6 [51.1-61.3]; 52.5 [44.2-55.3]). The language and executive deficits in paramedian thalamic stroke patients almost completely recovered during follow-up. Intriguingly, significant deficits in verbal memory (44.7 [41.5-51.9]), language (47.5 [41.8-54.1]), and executive functions (48.2 [46.2-59.7]) were found in inferolateral thalamic stroke patients at 1 month compared with controls (50.5 [46.7-59.9]; 57.0 [51.2-62.9]; 57.4 [51.2-60.7]). Language, but not executive deficits persisted during follow-up. Voxel-based lesion-symptom mapping revealed an association of verbal memory deficits with anterior thalamus lesions and an association of non-verbal memory, language, and executive deficits with lesions at the anterior/paramedian/inferolateral border. CONCLUSIONS All 3 stroke topographies exhibited significant deficits in diverse cognitive domains, which recovered to a different degree depending on the stroke localization. Our study emphasizes the need for comprehensive neuropsychological diagnostics to secure adequate patient rehabilitation

Phase anomalies in Talbot light carpets of selfimages

An interesting feature of light fields is a phase anomaly, which occurs on the optical axis when light is converging as in a focal spot. Since in Talbot images the light is periodically confined in both transverse and axial directions, it remains an open question whether at all and to which extent the phase in the Talbot images sustains an analogous phase anomaly. Here, we investigate experimentally and theoretically the anomalous phase behavior of Talbot images that emerge from a 1D amplitude grating with a period only slightly larger than the illumination wavelength. Talbot light carpets are observed close to the grating. We concisely show that the phase in each of the Talbot images possesses an anomalous axial shift. We show that this phase shift is analogous to a Gouy phase of a converging wave and occurs due to the periodic light confinement caused by the interference of various diffraction orders. Longitudinal-differential interferometry is used to directly demonstrate the axial phase shifts by comparing Talbot images phase maps to a plane wave. Supporting simulations based on rigorous diffraction theory are used to explore the effect numerically. Numerical and experimental results are in excellent agreement. We discover that the phase anomaly, i.e., the difference of the phase of the field behind the grating to the phase of a referential plane wave, is an increasing function with respect to the propagation distance. We also observe within one Talbot length an irregular wavefront spacing that causes a deviation from the linear slope of the phase anomaly. We complement our work by providing an analytical model that explains these features of the axial phase shift

Mechanism of Immediate Recurrences of Atrial Fibrillation After Restoration of Sinus Rhythm

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74034/1/j.1540-8159.2004.00389.x.pd

Randomized Comparison of Bipolar versus Unipolar Plus Bipolar Recordings During Segmental Ostial Ablation of Pulmonary Veins

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73720/1/j.1540-8167.2002.00851.x.pd