Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

Distribution of Eigenvalues for the Modular Group

The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.Comment: 72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Autho

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Major flaws in conflict prevention policies towards Africa : the conceptual deficits of international actors’ approaches and how to overcome them

Current thinking on African conflicts suffers from misinterpretations oversimplification, lack of focus, lack of conceptual clarity, state-centrism and lack of vision). The paper analyses a variety of the dominant explanations of major international actors and donors, showing how these frequently do not distinguish with sufficient clarity between the ‘root causes’ of a conflict, its aggravating factors and its triggers. Specifically, a correct assessment of conflict prolonging (or sustaining) factors is of vital importance in Africa’s lingering confrontations. Broader approaches (e.g. “structural stability”) offer a better analytical framework than familiar one-dimensional explanations. Moreover, for explaining and dealing with violent conflicts a shift of attention from the nation-state towards the local and sub-regional level is needed.Aktuelle Analysen afrikanischer Gewaltkonflikte sind häufig voller Fehlinterpretationen (Mangel an Differenzierung, Genauigkeit und konzeptioneller Klarheit, Staatszentriertheit, fehlende mittelfristige Zielvorstellungen). Breitere Ansätze (z. B. das Modell der Strukturellen Stabilität) könnten die Grundlage für bessere Analyseraster und Politiken sein als eindimensionale Erklärungen. häufig differenzieren Erklärungsansätze nicht mit ausreichender Klarheit zwischen Ursachen, verschärfenden und auslösenden Faktoren. Insbesondere die richtige Einordnung konfliktverlängernder Faktoren ist in den jahrzehntelangen gewaltsamen Auseinandersetzungen in Afrika von zentraler Bedeutung. Das Diskussionspapier stellt die große Variationsbreite dominanter Erklärungsmuster der wichtigsten internationalen Geber und Akteure gegenüber und fordert einen Perspektivenwechsel zum Einbezug der lokalen und der subregionalen Ebene für die Erklärung und Bearbeitung gewaltsamer Konflikte

Design of an Agile Unmanned Combat Vehicle - A Product of the DARPA UGCV Program

The unmanned ground combat vehicle (UGCV) design evolved by the SAIC team on the DARPA UGCV Program is summarized in this paper. This UGCV design provides exceptional performance against all of the program metrics and incorporates key attributes essential for high performance robotic combat vehicles. This performance includes protection against 7.62 mm threats, C130 and CH47 transportability, and the ability to accept several relevant weapons payloads, as well as advanced sensors and perception algorithms evolving from the PerceptOR program. The UGCV design incorporates a combination of technologies and design features, carefully selected through detailed trade studies, which provide optimum performance against mobility, payload, and endurance goals without sacrificing transportability, survivability, or life cycle cost. The design was optimized to maximize performance against all Category I metrics. In each case, the performance of this design was validated with detailed simulations, indicating that the vehicle exceeded the Category I metrics. Mobility metrics were analyzed using high fidelity VisualNastran vehicle models, which incorporate the suspension control algorithms and controller cycles times. DADS/Easy 5 3-D models and ADAMS simulations were also used to validate vehicle dynamics and control algorithms during obstacle negotiation

Characterization of traverse slippage experienced by Spirit rover on Husband Hill at Gusev crater

Spirit rover experienced significant slips traversing Husband Hill. This paper analyzes the slippage Spirit experienced from Sol 154 to Sol 737. Slippage with respect to terrain type and slope is computed using data downlinked from the rover, rover position, and orientation estimations from visual odometry (VO) and photogrammetry based bundle adjustment (BA) method. Accumulated slippage reached a maximum of 83.86 m on Sol 648. However, as Spirit descended into the Inner Basin, the direction of slippage reversed, and accumulated slippage approached zero by the end of the entire traverse. Eight local regions with significant slips and nineteen traverse segments have been analyzed. Slippage was found to be highly correlated to slope direction and magnitude; the reverse of slope directions in the ascending and descending portions of the traverse proves to be the main contributor to the observed cancellation of slippage. While the horizontal component of the slippage almost canceled out, the difference in elevation continually accumulated, mainly during the ascent. In general, long traverse segments created more slips than short ones. This is reflected in both the accumulated and individual slippages. In considering the four major Mars terrain types, Spirit performed best on bedrock, managing to drive on slopes close to 30°. Fine-grain surfaces were the most challenging; though progress was made on slopes up to 15°, slippages of over 100% (more slippage than distance traveled) occurred for short segments. The results of this work can be incorporate into a traverse planning framework in which rover slippage is minimized. Results can be employed in landed planetary missions for precision navigation to avoid potentially dangerous regions by considering expected slippage