Recently, Abraham and Delmas constructed the distributions of super-critical Lévy trees truncated at a fixed height by connecting super-critical Lévy trees to (sub)critical Lévy trees via a martingale transformation. A similar relationship also holds for discrete Galton-Watson trees. In this work, using the existing works on the convergence of contour functions of (sub)critical trees, we prove ...

The performance of block-matching sub-pixel motion estimation algorithms under the adverse conditions of image undersampling and additive noise is studied empirically. This study is motivated by the requirement for reliable subpixel accuracy motion estimates for motion compensated observation models used in multi-frame super-resolution image reconstruction. Idealized test functions which includ...

Metazoan genes are embedded in a rich milieu of regulatory information that often includes multiple enhancers possessing overlapping activities. In this study, we employ quantitative live imaging methods to assess the function of pairs of primary and shadow enhancers in the regulation of key patterning genes-knirps, hunchback, and snail-in developing Drosophila embryos. The knirps enhancers exh...

We present a new far-field super-resolution imaging approach called compressive spatial to spectral transformation microscopy (CSSTM). The transformation encodes the high-resolution spatial information to a spectrum through illuminating sub-diffraction-limited and wavelength-dependent patterns onto an object. The object is reconstructed from scattering spectrum measurements in the far field. Th...