We study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter. Next, we show that the problem of computing a minimum weight cover of points by weighted halfplanes (witho...

background access to appropriate images of fetal brain can greatly assist to diagnose of probable abnormalities. the aim of this study was to compare the suitability of t2-true fast imaging with steady state free precession (t2-trufi), and t2-half-fourier acquisition single-shot turbo spin-echo (t2- haste( magnetic resonance imaging (mri) to extract the fetal brain using the level set algorithm...

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible ge...

In this paper a general algorithm to find the boundaries of value sets bounded by elliptic arcs is developed. This algorithm uses a generalized line-sweep search procedure to extract the value set boundary from a set of generalized polygons describing the image of the bounding set or the extrema1 segments of the plant. The advantage of this approach is that , when the uncertainty is affine, it ...

We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold covering of the plane with its translates is decomposable into two disjoint coverings of the whole plane. Pach conjectured that every convex set is...

The card game SET can be modeled by four-dimensional vectors over Z3. These vectors correspond to points in the affine four-space of order three (AG(4, 3)), where lines correspond to SETs, and in the affine plane of order nine (AG(2, 9)). SETless collections and other aspects of the game of SET will be explored through caps in AG(4, 3) and conics in AG(2, 9).

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ...