We study classical and quantum caustics for systems with quadratic Lagrangians of the form L = 1 2 ẋ − 1 2 λ(t)x − μ(t)x. After deriving the transition amplitude on caustics in a closed form, we consider the Gaussian slit experiment and point out that the focusing around caustics is stabilized against initial momentum fluctuations by quantum effect. PACS codes: 02.30.Hg; 03.65.-w; 03.65.Sq

First order random graphs as introduced by Wong are a promising tool for structure-based classi$cation. Their complexity, however, hampers their practical application. We describe an extension to $rst order random graphs which uses continuous Gaussian distributions to model the densities of all random elements in a random graph. These First Order Gaussian Graphs (FOGGs) are shown to have severa...