Massless geodesics in AdS5×Y(p,q)AdS_5\times Y(p,q) as a superintegrable system

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusion

Parkin Deficiency Delays Motor Decline and Disease Manifestation in a Mouse Model of Synucleinopathy

In synucleinopathies, including Parkinson's disease, partially ubiquitylated α-synuclein species phosphorylated on serine 129 (PS129-α-synuclein) accumulate abnormally. Parkin, an ubiquitin-protein ligase that is dysfunctional in autosomal recessive parkinsonism, protects against α-synuclein-mediated toxicity in various models

Generalizations of the short pulse equation

We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation