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The relation between random normal matrices and conformal map-pings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.
We present a nonparametric regression method for denoising 3-D image sequences acquired via fluorescence microscopy. The proposed method exploits the redundancy of the 3-D+time information to improve the signal-to-noise ratio of images corrupted by Poisson-Gaussian noise. A variance stabilization transform is first applied to the image-data to remove the… (More)
We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined by the area of its interior domain and its exterior harmonic moments which are all given as parameters of the… (More)
The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a… (More)
We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of non-convex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in… (More)
Optical coherence tomography (OCT) and photoacoustic tomography are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform photoacoustic tomography and OCT imaging at once. In this paper, we present a mathematical model describing the dual experiment. Because OCT is… (More)