Improved time-decay for a class of scaling critical electromagnetic Schr\"odinger flows

We consider a Schr\"odinger hamiltonian $H(A,a)$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positive definite. We prove the following: if $\|e^{-itH(A,a)}\|_{L^1\to L^\infty}\lesssim t^{-n/2}$, then $\||x|^{-g(n)}e^{-itH(A,a)}|x|^{-g(n)}\|_{L^1\to L^\infty}\lesssim t^{-n/2-g(n)}$, $g(n)$ being a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$. We prove similar results also for the heat semi-group generated by $H(A,a)$

Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows

We consider a Schr\"odinger hamiltonian $H$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positively definite. We prove the following: if $\|e^{-itH}\|_{L^1\to L^\infty}\leq Ct^{-n/2}$, then $\||x|^{-g(n)}e^{-itH}|x|^{-g(n)}\|_{L^1\to L^\infty}\leq Ct^{-n/2-g(n)}$, being $g(n)$ a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$

Random Forests for Real Time 3D Face Analysis

We present a random forest-based framework for real time head pose estimation from depth images and extend it to localize a set of facial features in 3D. Our algorithm takes a voting approach, where each patch extracted from the depth image can directly cast a vote for the head pose or each of the facial features. Our system proves capable of handling large rotations, partial occlusions, and the noisy depth data acquired using commercial sensors. Moreover, the algorithm works on each frame independently and achieves real time performance without resorting to parallel computations on a GPU. We present extensive experiments on publicly available, challenging datasets and present a new annotated head pose database recorded using a Microsoft Kinec