1 Optimality theorems for JL Yesterday we saw for MJL that we could achieve target dimension m = O(ε −2 log N), and for DJL we could achieve m = O(ε −2 log(1/δ)). The following theorems tell us that not much improvement is possible for MJL, and for DJL we have the optimal bound. Theorem 1 ([Alo03]). For any N > 1 and ε < 1/2, there exist N + 1 points in R N such that achieving the MJL guarantee...

In this paper we present a method for reading a watermark from a dual layer hologram image with a digital camera. Here the base of the hologram out of which the hologram was designed is a binary image. The hologram obtained is placed on a planar surface and an image is captured from the hologram by setting up a light source and a digital camera on appropriate distances and angles relative to th...

The measurement of scalar fluxes employing the eddy covariance method is a widely used experimental approach, for which the flow distortion due to obstacles (e.g., sensor mounts and mast) is a well-known but not fully solved problem. In order to reduce flow distortion we installed a sonic anemometer in a surface-normal orientation relative to the terrain slope, and a second instrument in a vert...

Introduction:  Image  distortion  is  one  of  the  major  problems  of  magnetic  resonance  imaging  (MRI) for use in 3DMRI, velocity MRI, FMRI and radiotherapy treatment planning (RTTP). It is  widely known that the most obvious effect of the inhomogenity of the magnetic fields and the  nonlinearity  of  the  gradient  is  the  Geometric  Distortion  of  MR  tomograms.  In  this  study,  the...

We present a framework for shape alignment that generalizes several existing methods. We assume that the shape is a closed genus zero surface. Our framework requires a diffeomorphic surface mapping to the 2-sphere which preserves rotation. Our similarity measure is a global spherical cross-correlation function of surface-intrinsic scalar attributes, weighted by the cross-correlation of the para...