We show the existence of ε-nets of size O`1 ε log log 1 ε´f or planar point sets and axis-parallel rectangular ranges. The same bound holds for points in the plane with "fat" triangular ranges, and for point sets in R 3 and axis-parallel boxes; these are the first known non-trivial bounds for these range spaces. Our technique also yields improved bounds on the size of ε-nets in the more general context considered by Clarkson and Varadarajan. For example, we show the existence of ε-nets of size O`1 ε log log log 1 ε´f or the dual range space of "fat" regions and planar point sets (where the regions are the ground objects and the ranges are subsets stabbed by points). Plugging our bounds into the technique of Brönnimann and Goodrich, we obtain improved approximation factors (computable in randomized polynomial time) for the hitting set or the set cover problems associated with the corresponding range spaces.

This study was undertaken to review our approach to diagnosis and treatment in a series of 11 patients (mean age 8.2 years) with primary pyomyositis, who had neither an underlying disease nor a compromised immune system. Nine of the children had positive blood cultures, Staphylococcus aureus (eight) and Streptococcus group A (one). The sites of infection were iliopsoas (four), obturator (two), hip adductors (two), levator scapula (one), thoracolumbar paraspinal (one) and gastrocnemius (one) muscles. Antibiotic treatment was initially intravenous, followed by oral administration. Of five patients with evidence of abscess formation, three underwent percutaneous drainage, whereas two required open surgical drainage. The infection resolved completely without any sequela in 10 children. One patient who developed acute compartment syndrome showed late signs of osteonecrosis of the tibial shaft segment.

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