Unlocking the Axion-Dilaton in 5D Supergravity

We revisit supersymmetric solutions to five dimensional ungauged N=1 supergravity with dynamic hypermultiplets. In particular we focus on a truncation to the axion-dilaton contained in the universal hypermultiplet. The relevant solutions are fibrations over a four-dimensional Kahler base with a holomorphic axion-dilaton. We focus on solutions with additional symmetries and classify Killing vectors which preserve the additional structure imposed by supersymmetry; in particular we extend the existing classification of solutions with a space-like U(1) isometry to the case where the Killing vector is rotational. We elaborate on general geometrical aspects which we illustrate in some simple examples. We especially discuss solutions describing the backreaction of M2-branes, which for example play a role in the black hole deconstruction proposal for microstate geometries.Comment: 48 pages + appendices, 5 figure

FLUX SWITCHING IN MULTIPATH CORES REPT. 2

Flux switching in multipath magnetic core

Trifocal Relative Pose from Lines at Points and its Efficient Solution

We present a new minimal problem for relative pose estimation mixing point features with lines incident at points observed in three views and its efficient homotopy continuation solver. We demonstrate the generality of the approach by analyzing and solving an additional problem with mixed point and line correspondences in three views. The minimal problems include correspondences of (i) three points and one line and (ii) three points and two lines through two of the points which is reported and analyzed here for the first time. These are difficult to solve, as they have 216 and - as shown here - 312 solutions, but cover important practical situations when line and point features appear together, e.g., in urban scenes or when observing curves. We demonstrate that even such difficult problems can be solved robustly using a suitable homotopy continuation technique and we provide an implementation optimized for minimal problems that can be integrated into engineering applications. Our simulated and real experiments demonstrate our solvers in the camera geometry computation task in structure from motion. We show that new solvers allow for reconstructing challenging scenes where the standard two-view initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while most authors were in residence at Brown University's Institute for Computational and Experimental Research in Mathematics -- ICERM, in Providence, R