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Consider a set of n points in d-dimensional Euclidean space, d 2, each of which i s continuously moving along a given individual trajectory. A t e a c h instant in time, the points de ne a Voronoi diagram. As the points move, the Voronoi diagram changes continuously, but at certain critical instants in time, topological events occur that cause a change in the Voronoi diagram. In this paper, we present a method of maintaining the Voronoi diagram over time, while showing that the number of topological events has an upper bound of O(n d s (n)), where s (n) i s t h e m a x i m um length of a (n s)-Davenport-Schinzel sequence AgShSh 89, DaSc 65] and s is a constant depending on the motions of the point sites. Our results are a linear-factor improvement o ver the naive O(n d+2 ) upper bound on the number of topological events.In addition, we show that if only k points are moving (while leaving the other n ; k points xed), there is an upper bound of O(kn d;1 s (n) + ( n ;k) d s (k)) on the number of topological events.We give a n umerically stable algorithm for the update of the topological structure of the Voronoi diagram, using only O(log n) time per event (which i s w orst-case optimal per event).

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Different immunologic parameters were measured in cord blood to test their usefulness in the early diagnosis of early-onset sepsis. Cord blood levels of circulating intercellular adhesion molecule-1 (cICAM-1), interleukin-6 (IL-6) and interleukin-8 (IL-8) were significantly elevated in septic compared to nonseptic neonates. No significant difference between either population was seen for cord blood C3a and elastase-α₁-proteinase inhibitor complex (Eα₁PI). Measured concentrations of cICAM-1, IL-6 and IL-8 in fetal and maternal blood did not correlate, indicating that the neonate’s response to sepsis is clearly different from the mother. Our data suggest that cord blood measurements of cICAM-1, IL-6 and IL-8 might be useful in identifying neonates with early-onset sepsis.