The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

Surface-acoustic-wave counterflow micropumps for on-chip liquid motion control in two-dimensional microchannel arrays

Fully controlled liquid injection and flow in hydrophobic polydimethylsiloxane (PDMS) two-dimensional microchannel arrays based on on-chip integrated, low-voltage-driven micropumps are demonstrated. Our architecture exploits the surface-acoustic-wave (SAW) induced counterflow mechanism and the effect of nebulization anisotropies at crossing areas owing to lateral propagating SAWs. We show that by selectively exciting single or multiple SAWs, fluids can be drawn from their reservoirs and moved towards selected positions of a microchannel grid. Splitting of the main liquid flow is also demonstrated by exploiting multiple SAW beams. As a demonstrator, we show simultaneous filling of two orthogonal microchannels. The present results show that SAW micropumps are good candidates for truly integrated on-chip fluidic networks allowing liquid control in arbitrarily shaped two-dimensional microchannel arrays.

Combining 3D tracking and surgical instrumentation to determine the stiffness of spinal motion segments: a validation study

The spine is a complex structure that provides motion in three directions: flexion and extension, lateral bending and axial rotation. So far, the investigation of the mechanical and kinematic behavior of the basic unit of the spine, a motion segment, is predominantly a domain of in vitro experiments on spinal loading simulators. Most existing approaches to measure spinal stiffness intraoperatively in an in vivo environment use a distractor. However, these concepts usually assume a planar loading and motion. The objective of our study was to develop and validate an apparatus, that allows to perform intraoperative in vivo measurements to determine both the applied force and the resulting motion in three dimensional space. The proposed setup combines force measurement with an instrumented distractor and motion tracking with an optoelectronic system. As the orientation of the applied force and the three dimensional motion is known, not only force-displacement, but also moment-angle relations could be determined. The validation was performed using three cadaveric lumbar ovine spines. The lateral bending stiffness of two motion segments per specimen was determined with the proposed concept and compared with the stiffness acquired on a spinal loading simulator which was considered to be gold standard. The mean values of the stiffness computed with the proposed concept were within a range of ±15% compared to data obtained with the spinal loading simulator under applied loads of less than 5 Nm.

Dose modulated retrospective ECG-gated versus non-gated 64-row CT angiography of the aorta at the same radiation dose: Comparison of motion artifacts, diagnostic confidence and signal-to-noise-ratios

To compare ECG-gated and non-gated CT angiography of the aorta at the same radiation dose, with regard to motion artifacts (MA), diagnostic confidence (DC) and signal-to-noise-ratios (SNRs).

Interhemispheric connections shape subjective experience of bistable motion

The right and left visual hemifields are represented in different cerebral hemispheres and are bound together by connections through the corpus callosum. Much has been learned on the functions of these connections from split-brain patients [1-4], but little is known about their contribution to conscious visual perception in healthy humans. We used diffusion tensor imaging and functional magnetic resonance imaging to investigate which callosal connections contribute to the subjective experience of a visual motion stimulus that requires interhemispheric integration. The "motion quartet" is an ambiguous version of apparent motion that leads to perceptions of either horizontal or vertical motion [5]. Interestingly, observers are more likely to perceive vertical than horizontal motion when the stimulus is presented centrally in the visual field [6]. This asymmetry has been attributed to the fact that, with central fixation, perception of horizontal motion requires integration across hemispheres whereas perception of vertical motion requires only intrahemispheric processing [7]. We are able to show that the microstructure of individually tracked callosal segments connecting motion-sensitive areas of the human MT/V5 complex (hMT/V5+; [8]) can predict the conscious perception of observers. Neither connections between primary visual cortex (V1) nor other surrounding callosal regions exhibit a similar relationship.