Optimization-based solutions to constrained trajectory-tracking and path-following problems

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2012

Hydrogen interaction with supermartensitic stainless steel studied by energy dispersive X-ray diffraction

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2015

Robot trajectory optimization for relaxed effective tasks

Magdeburg, Univ., Fak. für Informatik, Diss., 2015

The history of creation, or, The development of the earth and its inhabitants by the action of natural causes : a popular exposition of the doctrine of evolution in general, and of that of Darwin, Goethe and Lamarck in particular / from the German of Ernst Haeckel ; the translation rev. by E. Ray Lankester.

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Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Periodic orbits in complex Abel equation

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Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Subsequent Trajectory

Combined media on photographic paper. 89” x 35⅝”

Dynamics of the third order Lyness' difference equation

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The equation xpyq=zr and groups that act freely on Λ-trees

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Non-assisted versus neuro-navigated and XperCT-guided external ventricular catheter placement: a comparative cadaver study.

BACKGROUND AND PURPOSE: Accurate placement of an external ventricular drain (EVD) for the treatment of hydrocephalus is of paramount importance for its functionality and in order to minimize morbidity and complications. The aim of this study was to compare two different drain insertion assistance tools with the traditional free-hand anatomical landmark method, and to measure efficacy, safety and precision. METHODS: Ten cadaver heads were prepared by opening large bone windows centered on Kocher's points on both sides. Nineteen physicians, divided in two groups (trainees and board certified neurosurgeons) performed EVD insertions. The target for the ventricular drain tip was the ipsilateral foramen of Monro. Each participant inserted the external ventricular catheter in three different ways: 1) free-hand by anatomical landmarks, 2) neuronavigation-assisted (NN), and 3) XperCT-guided (XCT). The number of ventricular hits and dangerous trajectories; time to proceed; radiation exposure of patients and physicians; distance of the catheter tip to target and size of deviations projected in the orthogonal plans were measured and compared. RESULTS: Insertion using XCT increased the probability of ventricular puncture from 69.2 to 90.2 % (p = 0.02). Non-assisted placements were significantly less precise (catheter tip to target distance 14.3 ± 7.4 mm versus 9.6 ± 7.2 mm, p = 0.0003). The insertion time to proceed increased from 3.04 ± 2.06 min. to 7.3 ± 3.6 min. (p < 0.001). The X-ray exposure for XCT was 32.23 mSv, but could be reduced to 13.9 mSv if patients were initially imaged in the hybrid-operating suite. No supplementary radiation exposure is needed for NN if patients are imaged according to a navigation protocol initially. CONCLUSION: This ex vivo study demonstrates a significantly improved accuracy and safety using either NN or XCT-assisted methods. Therefore, efforts should be undertaken to implement these new technologies into daily clinical practice. However, the accuracy versus urgency of an EVD placement has to be balanced, as the image-guided insertion technique will implicate a longer preparation time due to a specific image acquisition and trajectory planning.

Creation of an Age-Adjusted, Dual-Energy X-ray Absorptiometry-Derived Trabecular Bone Score Curve for the Lumbar Spine in Non-Hispanic US White Women.

The trabecular bone score (TBS, Med-Imaps, Pessac, France) is an index of bone microarchitecture texture extracted from anteroposterior dual-energy X-ray absorptiometry images of the spine. Previous studies have documented the ability of TBS of the spine to differentiate between women with and without fractures among age- and areal bone mineral density (aBMD)-matched controls, as well as to predict future fractures. In this cross-sectional analysis of data collected from 3 geographically dispersed facilities in the United States, we investigated age-related changes in the microarchitecture of lumbar vertebrae as assessed by TBS in a cohort of non-Hispanic US white American women. All subjects were 30 yr of age and older and had an L1-L4aBMDZ-score within ±2 SD of the population mean. Individuals were excluded if they had fractures, were on any osteoporosis treatment, or had any illness that would be expected to impact bone metabolism. All data were extracted from Prodigy dual-energy X-ray absorptiometry devices (GE-Lunar, Madison, WI). Cross-calibrations between the 3 participating centers were performed for TBS and aBMD. aBMD and TBS were evaluated for spine L1-L4 but also for all other possible vertebral combinations. To validate the cohort, a comparison between the aBMD normative data of our cohort and US non-Hispanic white Lunar data provided by the manufacturer was performed. A database of 619 non-Hispanic US white women, ages 30-90 yr, was created. aBMD normative data obtained from this cohort were not statistically different from the non-Hispanic US white Lunar normative data provided by the manufacturer (p = 0.30). This outcome thereby indirectly validates our cohort. TBS values at L1-L4 were weakly inversely correlated with body mass index (r = -0.17) and weight (r = -0.16) and not correlated with height. TBS values for all lumbar vertebral combinations decreased significantly with age. There was a linear decrease of 16.0% (-2.47 T-score) in TBS at L1-L4 between 45 and 90 yr of age (vs. -2.34 for aBMD). Microarchitectural loss rate increased after age 65 by 50% (-0.004 to -0.006). Similar results were obtained for other combinations of lumbar vertebra. TBS, an index of bone microarchitectural texture, decreases with advancing age in non-Hispanic US white women. Little change in TBS is observed between ages 30 and 45. Thereafter, a progressive decrease is observed with advancing age. The changes we observed in these American women are similar to that previously reported for a French population of white women (r(2) > 0.99). This reference database will facilitate the use of TBS to assess bone microarchitectural deterioration in clinical practice.