Natural orders for asymmetric space–time coding: minimizing the discriminant

Information-theoretic natural ultraviolet cutoff for spacetime.

Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can. It has been shown that the amplitudes phi(x(n)) that a field takes at a generic discrete set of points x(n) can be sufficient to reconstruct the field phi(x) for all x, namely, if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sa...

Minimizing Multi-zone Orders in the Correlated Storage Assignment Problem

To my parents for all their support iii ACKNOWLEDGEMENTS First and foremost, I would like to thank my parents for all their support during my time in graduate school. Without everything they have done for me during my time at Georgia Tech and well before, I would not have gotten to this point. I also want to thank my brother Chaim for his support. My primary advisor, Gunter Sharp, helped me def...

Approximation Orders for Natural Splines in Arbitrary

Asymmetric binary tree coding for contour images

We consider the coding of featured contours, i.e. texture, object or motion boundaries in images. The MPEG-4 and MPEG-7 video coding standards provide for a content-based representation of video information, so efficient coding of boundaries can play an important role. We propose a new coding scheme that uses an asymmetric binary tree. We show that the new scheme outperforms conventional quadtr...

The database of interval orders difficult for the jump number minimizing algorithms

The problems of scheduling jobs on a single machine subject to precedence constraints can often be modelled as the jump number problem for posets, where a linear extension of a given partial order is to be found which minimizes the number of noncomparabilities. In this paper, we are investigating a restricted class of posets, called interval orders, admitting approximation algorithms for the ju...