A collection C of balls in R is δ-inflatable if it is isometric to the intersection U ∩ E of some d-dimensional affine subspace E with a collection U of (d + δ)-dimensional balls that are disjoint and have equal radius. We give a quadratic-time algorithm to recognize 1-inflatable collections of balls in any fixed dimension, and show that recognizing δ-inflatable collections of d-dimensional bal...

This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls are drawn and their colors is changed according to the number of black balls among them.The limiting behaviour of the composition of the urn when both the tim...

Q balls are nontopological solitonic solutions to a wide class of field theories that possess global symmetries. Here we show that in these same theories there also exists a tower of novel composite Q-ball solutions where, within one composite Q ball, positive and negative charges coexist and swap at a frequency lower than the natural frequency of an individual Q ball. These charge-swapping Q b...

We consider a deposition model in which balls rain down at random towards a 2-dimensional surface, roll downwards over existing adsorbed balls, are adsorbed if they reach the surface, and discarded if not. We prove a spatial law of large numbers and central limit theorem for the ultimate number of balls adsorbed onto a large toroidal surface, and also for the number of balls adsorbed on the res...

The author of this document, Bill Harvey, was involved in many of the major developments in this field, and so this history is written from the author’s personal perspective. However, a more complete picture would require interviews with others so as to round out the total history of media optimization. In its present form, this document is solely intended for use in building internal consensus...

The Kneser-Poulsen conjecture says that if a finite collection of balls in the Euclidean space E is rearranged so that the distance between each pair of centers does not get smaller, then the volume of the union of these balls also does not get smaller. In this paper, we prove that if in the initial configuration the intersection of any two balls has common points with no more than d+1 other ba...

We consider the problem of approximating normal and feature sizes of a surface from point cloud data that may be noisy. These problems are central to many applications dealing with point cloud data. In the noise-free case, the normals and feature sizes can be approximated by the centers of a set of unique large Delaunay balls called polar balls. In presence of noise, polar balls do not necessar...

Imagine that there are two bins to which balls are added sequentially, and each incoming ball joins a bin with probability proportional to the pth power of the number of balls already there. A general result says that if p > 1/2, there almost surely is some bin that will have more balls than the other at all large enough times, a property that we call eventual leadership. In this paper, we comp...

To evaluate the influence of mass of ruminal contents on voluntary intake and ruminal function, five ruminally cannulated steers (550 kg) were fed an orchard grass hay diet ad libitum in a 5 x 5 Latin square experiment. The mass of ruminal contents was altered by adding varying weights of modified tennis balls to the rumen before the initiation of each 15-d experimental period. Treatments consi...

The modifications that have taken place within youth sports have made games, such as basketball, soccer, or tennis, easier for children to play. The purpose of this study was to determine the effects low compression (LC) tennis balls and scaled tennis courts had on the forehand groundstroke performance of children. The forehand groundstroke performances of eight subjects' (8.10 ± 0.74 yrs) usin...