Wicked metrics

There are various ways of defining the Wick rotation in a gravitational context. In order to preserve the manifold structure, it would be preferable to view it as an analytic continuation of the metric, instead of the coordinates. We focus on one very general definition and show that it is not always compatible with the additional requirements of preserving the field equations and the symmetries at global level. The counterexamples are the de Sitter and Schwarzschild metrics: requiring that their Euclidean continuations satisfy Einstein's equations and have the same number of Killing vectors, we find that the Euclidean metric cannot be defined on the original Lorentzian manifold but only on a submanifold. This phenomenon seems to be due to the existence of horizons

Alopecia Areata of Nonodontogenic Origin

ABSTRACT We report a case of alopecia areata in a 39-year-old female patient. Medical history revealed Hashimoto thyroiditis, while orthopantomogram suggested symptomless periodontal disease (tooth 27) with periodontal pocket 1.2 mm deep. Patient refused tooth extraction and applied minocyclin 4% and clobetasol propionate (Dermovatte) prescribed by a dermatologist. After 4 weeks hair started to regrow, patient refused to take therapy for any longer. We might conclude that stress rather than periodontal disease led to the localised hair loss

Patient Specific Biomechanical Model of the Brain: Application to Parkinson's disease procedure

International audienceno abstrac