In this paper we relate the problem of finding structures related to perfect matchings in bipartite graphs to a stochastic process similar to throwing balls into bins. Given a bipartite graph with n nodes on each side, we view each node on the left as having balls that it can throw into nodes on the right (bins) to which it is adjacent. If each node on the left throws exactly one ball and each ...

Let D be a set of n pairwise disjoint unit balls in R and P the set of their center points. A hyperplane H is an m-separator for D if each closed halfspace bounded by H contains at least m points from P . This generalizes the notion of halving hyperplanes, which correspond to n/2-separators. The analogous notion for point sets has been well studied. Separators have various applications, for ins...

The medial axis transform (or MAT) is a representation of an object as an in nite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a nite union of balls. Using this approximate MAT we de ne a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a suÆciently dense sam...

In this article, the failure behaviors of different solder balls and arrays used in a commercial produce were investigated experimentally and computationally. The results indicated that the effect of different solder balls and arrays on the failure behavior of Package-on-Package (PoP) structure cannot be ignored. For example, the failure mechanism of a structure with 2 15 solder balls could be ...

Soccer balls are typically constructed from 32 pentagonal and hexagonal panels. Recently, however, newer balls named Cafusa, Teamgeist 2, and Jabulani were respectively produced from 32, 14, and 8 panels with shapes and designs dramatically different from those of conventional balls. The newest type of ball, named Brazuca, was produced from six panels and will be used in the 2014 FIFA World Cup...

A single subject, withdrawal design was used to investigate the effects of therapy balls as seating on engagement and in-seat behavior of young children with Autism Spectrum Disorder (ASD). In addition, social validity was assessed to evaluate teachers' opinions regarding the intervention. During baseline and withdrawal (A phases) participants used their typical classroom seating device (chair,...

MSSM predicts the existence of Q-balls, some of which can be entirely stable. Both stable and unstable Q-balls can play an important role in cosmology. In particular, Affleck–Dine baryogenesis can result in a copious production of stable baryonic Q-balls, which can presently exist as a form of dark matter. CERN-TH/98-218 June, 1998 Talk presented at the Sixth International Symposium on Particle...

Suppose there is a bag containing red balls and blue balls. You would like to estimate the fraction of red balls in the bag. However, you are only allowed to sample randomly from the bag with replacement. The straightforward method is to make T random samples and use the fraction of red balls in the random samples as an estimate of the true fraction. The question is: how many samples are enough...

A volume image can be digitized in different grids, not only the cubic one. The fcc and bcc grids have many advantages, as they are more dense than the cubic one. The set of maximal balls in a shape in a volume image is a compact but complete description of the shape. The original set, identified by rules dependent on the metric used, can be further reduced, by observing that some balls are cov...

It is proposed to create materials with a desired refraction coefficient in a bounded domain D ⊂ R by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit volume around every point x ∈ D, i.e., their density distribution, is calculated, as well as the constant refraction coefficients in these balls. Embedding into D small bal...