Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical subjects, ranging from integration theory, algebraic topology, and algebraic geometry (toric varieties) to linear and combinatorial optimization. In this chapter we try to give a short introduction, pr...

This paper considers a broadcast system in which a single transmitter sends a common message and (independent) particular messages to K receivers over N unmatched parallel scalar Gaussian subchannels. For this system the set of all rate tuples that can be achieved via superposition coding and Gaussian signalling (SPCGS) can be parameterized by a set of power loads and partitions, and the bounda...

In this work, we identify the power-optimal wire spacing as a geometric program. Its solution is a vector of individual distances between the wires. To quantify the optimization potential by this method we model the output of a grid based router with a set of parallel wires. A comparison of the power values before and after geometric optimization shows that the optimization potential lies well ...

Let P be a set of n points in d-dimensional Euclidean space. A (k,eps)-kernel is a subset of P that, for every direction, epsilon-approximates the directional width of P, when k “outliers’’ can be ignored in that direction. We prove that small (k,eps)-kernels exist and describe efficient algorithms for computing them. Such kernels are instrumental in solving shape-fitting problems with k outlie...

introduction: image quality and accuracy of in vivo activity quantification in spect are affected by collimator penetration and scatter components, especially in high energy imaging. these phenomena highly depend on the collimator characteristic and photon energy. the presence of penetrated and scattered photons from collimator in spect images degrades spatial resolution, contrast and image qua...