Fragments in Gaussian Wave-Packet Dynamics with and without correlations

Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the description of light fragments with correlations. Utilizing either type of Gaussian wave functions, with or without correlations, however, we find that we cannot describe fragment formation in a dynamic situation. Composite fragments are only produced in simulations if they are present as clusters in the substructure of original nuclei. The difficulty is traced to the delocalization of wave functions during emission. Composite fragments are produced abundantly in the Gaussian molecular dynamics in the limit $\hbar \rightarrow 0$.Comment: 22 pages, revtex, 6 postscript figure

Dynamical fluctuations in the one particle density - comparison of different approaches

Diffusion coefficients are obtained from linear response functions and from the quantal fluctuation dissipation theorem. They are compared with the results of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well as the Boltzmann-Langevin theory. Sum rules related to conservation laws for total particle number, momentum and energy are demonstrated to hold true for fluctuations and diffusion coefficients in the quantum case.Comment: 23 pages, Latex, accepted for publication in Nucl. Phys.

Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms

We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete theoretical solution to the Phase Retrieval Problem for characteristic functions of convex bodies. The approach is via the closely related problem of reconstructing K from noisy measurements of its covariogram, the function giving the volume of the intersection of K with its translates. In the many known situations in which the covariogram determines a convex body, up to reflection in the origin and when the position of the body is fixed, our algorithms use O(k^n) noisy covariogram measurements to construct a convex polytope P_k that approximates K or its reflection -K in the origin. (By recent uniqueness results, this applies to all planar convex bodies, all three-dimensional convex polytopes, and all symmetric and most (in the sense of Baire category) arbitrary convex bodies in all dimensions.) Two methods are provided, and both are shown to be strongly consistent, in the sense that, almost surely, the minimum of the Hausdorff distance between P_k and K or -K tends to zero as k tends to infinity.Comment: Version accepted on the Journal of the American Mathematical Society. With respect to version 1 the noise model has been greatly extended and an appendix has been added, with a discussion of rates of convergence and implementation issues. 56 pages, 4 figure

Convergence of algorithms for reconstructing convex bodies and directional measures

We investigate algorithms for reconstructing a convex body $K$ in $\mathbb {R}^n$ from noisy measurements of its support function or its brightness function in $k$ directions $u_1,...,u_k$. The key idea of these algorithms is to construct a convex polytope $P_k$ whose support function (or brightness function) best approximates the given measurements in the directions $u_1,...,u_k$ (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, almost surely, $P_k$ tends to $K$ in the Hausdorff metric as $k\to\infty$. Here some mild assumptions on the sequence $(u_i)$ of directions are needed. Using results from the theory of empirical processes, estimates of rates of convergence are derived, which are first obtained in the $L_2$ metric and then transferred to the Hausdorff metric. Along the way, a new estimate is obtained for the metric entropy of the class of origin-symmetric zonoids contained in the unit ball. Similar results are obtained for the convergence of an algorithm that reconstructs an approximating measure to the directional measure of a stationary fiber process from noisy measurements of its rose of intersections in $k$ directions $u_1,...,u_k$. Here the Dudley and Prohorov metrics are used. The methods are linked to those employed for the support and brightness function algorithms via the fact that the rose of intersections is the support function of a projection body.Comment: Published at http://dx.doi.org/10.1214/009053606000000335 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mechanical properties of cells and matrix investigated by quantitative atomic force microscopy

Zellen und deren umgebende extrazelluläre Matrix (ECM) sind einer Vielzahl unterschiedlicher mechanischer Belastungen im Körper ausgesetzt. Daher ist der strukturelle Aufbau eines jeden Gewebes an die entsprechenden Anforderungen angepasst. Dabei spielen sowohl intrazellulär als auch extrazellulär Netzwerke aus Strukturproteinen eine maßgebliche Rolle: Intrazellulär bestimmt u.a. die Architektur des Aktin-Zytoskeletts die mechanischen Eigenschaften von Zellen, extrazellulär ist die mechanische Stabilität der extrazellulären Basalmembran (BM) im Wesentlichen durch ein Netzwerk aus Laminin determiniert. In dieser Arbeit wurde mittels Rasterkraftmikroskopie untersucht, auf welche Weise die Struktur dieser Netzwerke den Elastizitätsmodul der ECM, einzelner lebender Zellen und zellbeladener 3D-Hydrogele beeinflusst. Das Rasterkraftmikroskop (AFM) ermöglicht dabei die Untersuchung von Mikroelastizitäten mit einer hohen räumlichen Auflösung unter nahezu physiologischen Bedingungen. Im ersten Teil der Arbeit wurde gezeigt, dass die mechanischen Eigenschaften der BM durch das Protein Netrin-4 (Net-4) moduliert wird. Hierzu wurde Matrigel, ein Laminin-haltiges, ECM-basiertes Hydrogel, welches als artifizielle BM diente, mit zunehmenden Mengen des Proteins Net-4 versetzt. AFM-Indentationsmessungen zeigten eine quantitative Abnahme des Elastizitätsmoduls mit zunehmender Net-4 Konzentration. Dies bestätigt die postulierte Funktion von Net-4 als Regulator für die mechanischen Eigenschaften der BM und stützt die Hypothese, dass die Modulation der BM-Mechanik auf einer kompetitiven Bindung von Net-4 an die ternären Knotenpunkte beruht, an denen durch Verbindung von jeweils drei Laminin-Molekülen die Netzwerkbildung erfolgt. Im zweiten Teil der Arbeit wurde der Zusammenhang zwischen der Struktur des Aktin-Zytoskeletts und der lokalen Elastizität in lebenden Zellen mittels räumlich hochauflösender, quantitativer Rasterkraftmikroskopie, welche das schnelle und simultane Messen der Zelltopographie und des Elastizitätsmoduls einzelner Zellen ermöglicht, untersucht. Insgesamt konnten dadurch Elastizitätsprofile einzelner Zellen erstellt werden, wodurch sich eindeutig unterschiedliche Elastizitätsmoduln den unterschiedlichen Vernetzungsformen des Aktin-Zytoskeletts zuordnen ließen: Aktin-Netzwerke aus stark verzweigten Aktinfasern zeigten einen höheren Elastizitätsmodul, als Bereiche mit linearen und parallelen Fasern. Bei einer parallelen Anordnung der Fasern sinkt außerdem der Elastizitätsmodul mit zunehmendem Abstand zwischen den Fasern. ii Die Struktur des Aktin-Zytoskeletts wird dabei durch eine Vielzahl von Gerüstproteinen, wie z.B. α-Aktinin-1 (A1) und -4 (A4), bestimmt. Ein Knockout beider α-Aktinine resultierte in einem stark verzweigten basalen Aktin-Zytoskelett, welches sich kranzförmig um den Zellkern anordnete, sowie einem Verlust kernüberspannender dorsaler Aktinfasern, den sogenannten Aktinkappen. Bezogen auf die Topographie und den Elastizitätsmodul führte dies zu einer Art „Spiegelei“-Struktur: mittig waren diese Zellen hoch und weich, in der Peripherie jedoch flach und fest. Für A1 und A4 konnten außerdem unterschiedliche Funktionen in Bezug auf die Aktinarchitektur und damit die mechanischen Eigenschaften der Zellen identifiziert werden. A1 fördert das Ausbilden geradliniger basaler und dorsaler Aktinfasern. Durch das Vorhandensein von nur wenigen Aktinkappen ähneln die Zellen zwar dem Phänotyp von Wildtypzellen, insgesamt zeigen sie jedoch einen verringerten Elastizitätsmodul über den gesamten Bereich der Zelle. Im Gegensatz dazu fördert A4 die Quervernetzung der Aktinfasern. Dies resultierte ebenfalls peripher in einem netzartigen, flachen und festen sowie mittig in einem hohen und weichen Erscheinungsbild der Zellen. Die Struktur des Aktin-Zytoskeletts ändert sich außerdem durch natürliche Prozesse, wie das Altern von Zellen. Durch den Vergleich des Elastizitätsprofils und des Aktin-Zytoskeletts primärer, humaner Sehnenvorläuferzellen (TSPC) von jungen und älteren Patienten (Y-TSPC und A-TSPC) konnte gezeigt werden, dass diese strukturellen Veränderungen den Elastizitätsmodul der Zelle modellieren, und der Elastizitätsmodul somit als Biomarker für Zellalterung dienen kann. Im Vergleich zu Y-TSPCs zeigten die A-TSPCs einen höheren Elastizitätsmodul und dichter gepackte parallele Aktinfasern. Die Inhibition von ROCK 1 und 2 in A-TSPCs, führte wieder zu einem lose gepackten Aktin-Zytoskelett und damit zu einer Annäherung an die Struktur von Y-TSPCs. Auch diese „strukturelle Verjüngung“ manifestierte sich in einem verringerten Elastizitätsmodul, ähnlich dem von Y-TSPC Zellen. Schließlich wurde gezeigt, inwiefern Y- und A-TSPC Zellen die mechanischen Eigenschaften ihrer umgebenden Matrix beeinflussen können, indem diese in einem dreidimensionalen Polypeptid-basierten Hydrogel kultiviert und das Gel anschließend auf Veränderungen im Elastizitätsmodul hin untersucht wurde. Dabei konnte gezeigt werden, dass beide Zelltypen den Elastizitätsmodul der umgebenden Matrix deutlich erhöhen. Dieser Effekt war bei A-TSPCs deutlicher ausgeprägt als bei Y-TSPCs, was als weiteres Merkmal für Zellalterung gedeutet werden kann. Das Elastizitätsmodul könnte auch hier als Biomarker für Zellalterung dienen um zukünftig Gewebe mit jungen von Gewebe mit gealterten Zellen zu unterscheiden.Cells and their extracellular matrix (ECM) are exposed to a broad range of different mechanical loads in the body. For this reason, the structural composition of each tissue is adapted to its specific requirements. In this context, networks of structural proteins play a crucial role: for example, the architecture of the actin cytoskeleton determines the mechanical properties of cells and the mechanical stability of the extracellular basement membrane (BM) is determined mainly by a laminin network. In this thesis, atomic force microscopy (AFM), which allows the investigation of the microelasticity with a high spatial resolution under nearly physiological conditions, was used to investigate how the structure of these networks affects the Young’s modulus of the ECM, of single living cells and cell-laden 3D hydrogels. In the first part of this thesis, it was shown that the mechanical properties of the BM can be regulated by the protein Netrin-4 (Net-4). For this purpose, matrigel, a laminin-containing, ECM-based hydrogel, which served as an artificial BM, was supplemented with increasing amounts of the protein Net-4. AFM measurements revealed a quantitative decrease of the Young’s modulus with increasing Net-4 concentrations. This confirms the postulated function of Net-4 as a regulator for the mechanical properties of the BM and supports the hypothesis that the modulation of the BM-mechanics is based on competitive binding of Net-4 to the ternary nodes usually connecting three laminin molecules for network formation. In the second part of the thesis, the relationship between the structure of the actin cytoskeleton and the local elasticity in living cells was investigated by high-resolution, quantitative AFM, which enables to render the cell topography and the Young’s modulus simultaneously. Thereby, elasticity profiles of individual cells were generated, which identified different Young’s moduli for different actin fiber arrangements. Highly branched actin fibers revealed a higher Young’s modulus than regions with linear and parallel actin fibers. However, the Young’s modulus also decreases with an increasing fiber-to-fiber distance for parallel fibers. The structure of the actin cytoskeleton is governed by a large number of scaffolding proteins such as α-actinin-1 (A1) and -4 (A4). A knockout of both α-actinins caused a strongly branched basal actin cytoskeleton located around the cell nucleus, as well as a loss of dorsal actin fibers spanning over the nucleus, so-called actin caps. This results in a kind of "fried egg" morphology of the topography and the Young’s modulus: these cells were high and soft in the center, but flat and stiff in the periphery. iv Furthermore, different functions of A1 and A4 in regulating the actin architecture and thus the mechanical properties of the cells were identified. A1 promotes the formation of linear basal and dorsal actin fibers and therefore, the cells resemble the phenotype of wildtype cells. However, due to the presence of only a few actin caps, these cells showed a reduced Young’s modulus. In contrast, A4 promotes the cross-linking of the actin fibers. This caused highly branched peripheral actin fibers, resulting in flat and stiff as well as a high and soft parts of the cells. The structure of the actin cytoskeleton also changes by natural processes such as cell aging. Comparing the elasticity profile and the actin cytoskeleton of primary human tendon stem progenitor cells (TSPC) of young and aged patients (Y-TSPC and A-TSPC), revealed that structural changes of the actin structure are also reflected by the Young’s modulus. Thus, the Young’s modulus is a suitable biomarker for cell aging. Compared to Y-TSPCs, A-TSPCs revealed a higher Young’s modulus in combination with an increased density of parallel actin fibers. The inhibition of ROCK 1 and 2 in A-TSPCs induced a loosely packed actin cytoskeleton and thus an adaption of the actin structure back to that of Y-TSPCs. This "structural rejuvenation" was also manifested in a reduced Young’s modulus, similar to that of Y-TSPC cells. Finally, it was shown how Y- and A-TSPC cells influence the mechanical properties of their surrounding matrix. Therefore, Y- and A- TSPCs were cultivated in a 3D polypeptide-based hydrogel and the Young’s modulus of the gel was examined. Both cell types increased the Young’s modulus of their surrounding matrix. This effect was more evident in A-TSPCs than in Y-TSPCs, which can be considered to be a further characteristic of cell aging. Therefore, in the future, the Young’s modulus of 3D constructs could also serve as a biomarker for cell aging and allow to discriminate between young and aged tissue

Cross-sectional study assessing HIV related knowledge, attitudes and behavior in Namibian public sector employees in capital and regional settings

The study objective was to assess the current status of HIV knowledge, attitudes and behavior (KAB) among employees of Namibian ministries. As most HIV campaigning takes place in the capital of Windhoek, an additional aim was to compare Windhoek to four regions (Hardap, Erongo, Oshana, and Caprivi). Between January and March 2011 a cross-sectional survey was conducted in two Namibian ministries, with participants selected randomly from the workforce. Data collection was based on questionnaires. 832 participants were included in the study (51.6% male). Nearly 90% of participants reported to have been tested for HIV before. Knowledge about HIV transmission ranged from 67% to 95% of correct answers, with few differences between the capital and regions. However, a knowledge gap regarding HIV transmission and prevention was seen. In particular, we found significantly lower knowledge regarding transmission from mother-to-child during pregnancy and higher rate of belief in a supernatural role in HIV transmission. In addition, despite many years of HIV prevention activities, a substantial proportion of employees had well-known HIV risk factors including multiple concurrent partnership rates (21%), intergenerational sex (19%), and lower testing rates for men (82% compared to women with 91%)