Cosmic-Ray Rejection by Laplacian Edge Detection

Conventional algorithms for rejecting cosmic-rays in single CCD exposures rely on the contrast between cosmic-rays and their surroundings, and may produce erroneous results if the Point Spread Function (PSF) is smaller than the largest cosmic-rays. This paper describes a robust algorithm for cosmic-ray rejection, based on a variation of Laplacian edge detection. The algorithm identifies cosmic-rays of arbitrary shapes and sizes by the sharpness of their edges, and reliably discriminates between poorly sampled point sources and cosmic-rays. Examples of its performance are given for spectroscopic and imaging data, including HST WFPC2 images.Comment: Accepted for publication in the PASP (November 2001 issue). The algorithm is implemented in the program L.A.Cosmic, which can be obtained from http://www.astro.caltech.edu/~pgd/lacosmic

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

We present some open problems and obtain some partial results for spectral optimization problems involving measure, torsional rigidity and first Dirichlet eigenvalue.Comment: 18 pages, 4 figure

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits

Slow relaxation, dynamic transitions and extreme value statistics in disordered systems

We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase transition in these models to the extreme value statistics of the associated random energy landscape