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Diese Diplomarbeit befasst sich mit dem Arbenz-Embrechts-Puccetti-Algorithmus (AEP-Algorithmus) zur Berechnung der Verteilung von Summen abh��ngiger, nicht-negativer Zufallsvariablen f��r eine gegebene, absolut stetige, multivariate Verteilungsfunktion. Diese Berechnung ist von gro��er Bedeutung bei der Bestimmung eines Value-at-Risk basierten Eigenkapitalerfordernisses im operationellen Risikomanagement. F��r eine gegebene multivariate Verteilungsfunktion approximiert der Algorithmus das durch die Verteilungsfunktion induzierte Wahrscheinlichkeitsma�� auf einem Simplex durch eine endliche Summe der Wahrscheinlichkeitsma��e von Hyperw��rfeln. Die Ergebnisse des AEP-Algorithmus vergleichen wir mit den Ergebnissen numerischer Integrationsmethoden und Rekursion. Basierend auf den Aufbau adaptiver Integrationsmethoden konstruieren wir eine adaptive Version des AEP-Algorithmus mit dem Ziel die Geschwindigkeit zu erh��hen und dabei die gleiche Genauigkeit wie durch den Originalalgorithmus zu erzielen. Abschlie��end vergleichen wir die Resultate des adaptiven AEP-Algorithmus und des AEP-Algorithmus in Bezug auf Genauigkeit und die Anzahl der ben��tigten Unterteilungen., This thesis deals with the Arbenz-Embrechts-Puccetti algorithm (AEP algorithm) for the computation of the distribution of sums of dependent non-negative random variables with given absolutely continuous joint distribution. This calculation is of great interest in the determination of a Value-at-Risk based capital requirement in operational risk management. Given a joint distribution function, the algorithm approximates the probability measure induced by the distribution function on a simplex by a finite sum of the probability measures of hypercubes. We compare the results of AEP algorithm with the results of numerical integration methods and recursion. Based on the structure of adaptive integration methods we construct an adaptive version of the AEP algorithm. The aim of the adaption is to increase the speed, while maintaining the same accuracy as by the original algorithm. In conclusion, we compare the results of the AEP adaptive algorithm and the AEP algorithm in terms of accuracy and the number of subregions required.

Gedruckte Version im Universitätsverlag der TU Berlin erschienen, ISBN 978-3-7983-2396-4, ISSN 2193-6846 Patenschaften zwischen Schule und Stadt als Motor für eine soziale Stadtentwicklung Wie können SchülerInnen an der Konzeption ihrer gebauten Umwelt beteiligt werden und dabei einen neuen Austausch zwischen Schule und Stadt initiieren? Pfefferwerk Stadtkultur gGmbH und das Fachgebiet von Prof. Susanne Hofmann am Institut für Architektur der TU Berlin erproben unterschiedliche Modelle der Nutzerbeteiligung. Im Rahmen von Schule aktiv - Durchstarten im Brunnenviertel entwickeln ExpertInnen aus den Fachbereichen Architektur, Szenografie, Design und Pädagogik gemeinsam mit SchülerInnen unterschiedliche Konzepte der Raumgestaltung an der Ernst-Reuter-Sekundarschule (ERS) und der Gustav-Falke-Grundschule (GFS) im Berliner Wedding. Parallel dazu erforschen die Grund- und SekundarschülerInnen zusammen mit Architekturstudierenden die Ressourcen der Nachbarschaft und entwickeln experimentelle Formen für eine Vernetzung der Schule mit dem Stadtteil. Im gegenseitigen Austausch konzipieren sie architektonische Visionen für die Belebung der strikten Grenzen ihrer Schulen. Sie entdecken den öffentlichen Raum als nachbarschaftlichen Lernort und sie zeigen wie die Interessen der Jugendlichen als Imagefaktor ihres Stadtteils ihren Kiez über seine Grenzen hinaus bekannt machen können. Mentoring between school and city - Driving force for social urban development How can pupils contribute to the creation of their built environment and thereby initiate a new sort of exchange between schools and the city? Professor Susanne Hofmann of the Technical University Berlin and Pfefferwek Stadtkultur are testing different modes of user participation. As part of the project “Schule aktiv - Durchstarten im Brunnenviertel” experts in architecture, scenography, design and education will be working with pupils to develop different interior concepts for two schools, Ernst-Reuter-School and the Gustav-Falke Elementary School, in the Wedding neighbourhood, Berlin. In parallel, primary and secondary school pupils will be working together with architecture students to explore the area’s resources and develop experimental modes of networking between the school and local neighbourhood. Through mutual exchange they will develop an architectural vision for the school’s revitalisation and connection to its locality. They will investigate the possibilities of the public realm as a space for neighbourhood learning and demonstrate how the interests of young people can transform the identity of place, and thereby the wider perception of the neighbourhood.

The Cassini Visual and Infrared Mapping Spectrometer (VIMS) obtained data of Titan's surface from flybys performed during the last seven years. In the 0.8-5.2 µm range, these spectro-imaging data showed that the surface consists of a multivariable geological terrain hosting complex geological processes. The data from the seven narrow methane spectral "windows" centered at 0.93, 1.08, 1.27, 1.59, 2.03, 2.8 and 5 µm provide some information on the lower atmospheric context and the surface parameters that we want to determine. Atmospheric scattering and absorption need to be clearly evaluated before we can extract the surface properties. We apply here a statistical method [1, 2] and a radiative transfer method [3, 1] on three potentially "active" regions on Titan, i.e. regions possibly subject to change over time (in brightness and/or in color etc) [4]: Tui Regio (20°S, 130°W) [5], a 1,500-km long flow-like figure, Hotei Regio (26°S, 78°W) [6], a 700-km wide volcanic-like terrain, and Sotra Facula (15°S, 42°W) [7], a 235-km in diameter area. With our method of Principal Component Analysis (PCA) we have managed to isolate specific regions of distinct and diverse chemical composition. We have tested this method on the previously studied Sinlap crater [8], delimitating compositional heterogeneous areas compatible with the published conclusions by Le Mouélic et al. (2008). Our follow-up method focuses on retrieving the surface albedo of the three areas and of the surrounding terrains with different spectral response by applying a radiative transfer (RT) code. We have used as input most of the Cassini HASI and DISR measurements, as well as new methane absorption coefficients [9], which are important to evaluate the atmospheric contribution and to allow us to better constrain the real surface alterations, by comparing the spectra of these regions. By superposing these results onto the PCA maps, we can correlate composition and morphology. As a test case, we used our RT code to verify the varying brightness of Hotei Regio reported by other investigators based on models lacking proper simulation of the atmospheric absorption [10]. Even though we have used exactly the same dataset, we did not detect any significant surface albedo variations over time; this led us to revise the definition of "active" regions: even if these regions have not visually changed over the course of the Cassini mission, the determination of the chemical composition and the correlation with the morphological structures [11] observed in these areas do not rule out that past and/or ongoing cryovolcanic processes are still a possible interpretation. [1] Solomonidou, A. et al. (2011). Potentially active regions on Titan: New processing of Cassini/VIMS data. In preparation. [2] Stephan, K. et al. (2008). Reduction of instrument-dependent noise in hyperspectral image data using the principal component analysis: Applications to Galileo NIMS data. Planetary and Space Science 56, 406-419. [3] Hirtzig, M. et al. (2011). Applications of a new methane linelist to Cassini/VIMS spectra of Titan in the 1.28-5.2 µm range . In preparation. [4] Wall, s. D. et al. (2009). Cassini RADAR images at Hotei Arcus and western Xanadu, Titan: Evidence for geologically recent cryovolcanic activity. Journal of Geophysical Research 36, L04203, [5] Barnes, J.W. et al. (2006). Cassini observations of flow-like features in western Tui Regio, Titan. Geophysical Research Letters 33, L16204. [6] Soderblom, L.A. et al. (2009). The geology of Hotei Regio, Titan: Correlation of Cassini VIMS and RADAR. Icarus 204, 610-618. [7] Lopes, R.M.C. et al. (2010). Distribution and interplay of geologic processes on Titan from Cassini radar data. Icarus 205, 540-558. [8] Le Mouélic et al. (2008). Mapping and interpretation of Sinlap crater on Titan using Cassini VIMS and RADAR data. Journal of Geophysical Research 113, E04003. [9] Campargue, A. et al. (2011). An empirical line list for methane at 80 K and 296 K in the 1.26-1.71 µm region for planetary investigations. Application to Titan. Icarus. Submitted. [10] Nelson, R. et al (2009). Saturn's Titan: Surface change, ammonia, and implications for atmospheric and tectonic activity. Icarus 199, 429-441. [11] Solomonidou, A. et al. (2011). Possible morphotectonic features on Titan and their origin. Planetary and Space Science. Submitted.

We report a rare case of spontaneous rupture of the uterus in a 20 weeks pregnancy, which was treated surgically with a good outcome for the mother. The microscopic appearance of the uterus and the histologic examination of the rupture sites are compatible with invasive placenta with signs of acute of chronic infection and areas of syncytial infection of the uterus.