Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their monodromy, differential Galois group and the underlying rank-2 vector bundle. The latter is described in terms of elementary transforms. The question of its (semi)-stability is addressed.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Metric Learning for Image Registration

Image registration is a key technique in medical image analysis to estimate deformations between image pairs. A good deformation model is important for high-quality estimates. However, most existing approaches use ad-hoc deformation models chosen for mathematical convenience rather than to capture observed data variation. Recent deep learning approaches learn deformation models directly from data. However, they provide limited control over the spatial regularity of transformations. Instead of learning the entire registration approach, we learn a spatially-adaptive regularizer within a registration model. This allows controlling the desired level of regularity and preserving structural properties of a registration model. For example, diffeomorphic transformations can be attained. Our approach is a radical departure from existing deep learning approaches to image registration by embedding a deep learning model in an optimization-based registration algorithm to parameterize and data-adapt the registration model itself.Comment: 12 page

Reconciling leptogenesis with observable mu --> e gamma rates

We perform a detailed analysis of thermal leptogenesis in the framework of seesaw models which approximately conserve lepton number. These models are known to allow for large Yukawa couplings and a low seesaw scale in agreement with neutrino mass constraints, and hence to lead to large lepton flavour violating rates that can be probed experimentally. Although large Yukawa couplings lead to (inverse) decay rates much larger than the Hubble expansion rate, we show that the leptogenesis washout induced is generically small if the mass splitting between the right-handed neutrinos is small enough. As a result, large lepton flavour violating rates are compatible with successful leptogenesis. We emphasize that this scenario does not require any particular flavour structure. A small splitting is natural and radiatively stable in this context because it is protected by the lepton number symmetry.Comment: One section added, a few equations and sentences rewritten, references added, results unchange