One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shap...

We study the nonstationary solutions of Fokker–Planck equations associated to either stationary or non stationary quantum states. In particular, we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. As a first signficant application we pr...

In this note, we solve the Loewner equation in the upper halfplane with forcing function ξ(t), for the cases in which ξ(t) has a power-law dependence on time with powers 0, 1/2 and 1. In the first case the trace of singularities is a line perpendicular to the real axis. In the second case the trace of singularities can do three things. If ξ(t) = 2 √ κt, the trace is a straight line set at an an...

The asymptotic behavior of birth and death processes of particles in a compact space is analyzed. Births: Particles are created at rate λ+ and their location is independent of the current configuration. Deaths are due to negative particles arriving at rate λ − . The death of a particle occurs when a negative particle arrives in its neighborhood and kills it. Several killing schemes are consider...

The influence of the structural state on deformation mechanisms under large strains was investigated in a Cu – 2 wt.% Be alloy. Torque evolutions during straining exhibit serrations typical relaxations precipitation-hardened alloy, but not solid solution state. Microstructure characterization revealed that homogeneous led to strong grain size reduction (20 nm), while localization occurred preci...