Disparity and optical flow partitioning using extended Potts priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notion of asymptotically level stable (als) functions, we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of multipliers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole

Thermal Wightman functions of a massless scalar field are studied within the framework of a ``near horizon'' static background model of an extremal R-N black hole. This model is built up by using global Carter-like coordinates over an infinite set of Bertotti-Robinson submanifolds glued together. The analytical extendibility beyond the horizon is imposed as constraints on (thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It turns out that only the Bertotti-Robinson vacuum state, i.e. $T=0$, satisfies the above requirement. Furthermore the extension of this state onto the whole manifold is proved to coincide exactly with the vacuum state in the global Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem for the Minkowski space-time in terms of Wightman functions holds with vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum restricted to a Bertotti-Robinson region, resulting a pure state there, has vanishing entropy despite of the presence of event horizons. Some comments on the real extreme R-N black hole are given

Statistical Analysis of Different Muon-antineutrino->Electron-antineutrino Searches

A combined statistical analysis of the experimental results of the LSND and KARMEN \numubnueb oscillation search is presented. LSND has evidence for neutrino oscillations that is not confirmed by the KARMEN experiment. This joint analysis is based on the final likelihood results for both data sets. A frequentist approach is applied to deduce confidence regions. At a combined confidence level of 36%, there is no area of oscillation parameters compatible with both experiments. For the complementary confidence of 1-0.36=64%, there are two well defined regions of oscillation parameters (sin^2(2th),Dm^2) compatible with both experiments.Comment: 25 pages, including 10 figures, submitted to Phys. Rev.