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series method in Abate and Whitt [2] (the algorithm Euler exploiting Euler summation), although alternative methods could be used The inversion algorithm is remarkably fast; computation for each time point corresponds simply to a sum of 50 terms We provide numerical examples in Examples 1762 and 1781 Example 1781 is of special interest, because the level-holding-time distribution there is Pareto In Section 175 we show that in some cases we can avoid the inversion entirely and treat much larger models We can avoid the inversion if we can assume that the level holding times are relatively long compared to the times of interest for control Then we can apply a single-transition approximation, which amounts to assuming that the Markov chain is absorbing after one transition Then the conditional mean is directly expressible in terms of the level-holding-time distributions.

Alternatively, we can perform a two-transition approximation, which only involves one-dimensional convolution integrals In Section 176 we describe the value of having more detailed state information, speci cally the current ages of levels With heavy-tailed distributions, a large elapsed holding time means that a large remaining holding time is very likely; for examples see Duf eld and Whitt [14, Section 8] for background, and Harchol-Balter and Downey [21] for an application in another setting In Section 177 we turn to applications to capacity planning The idea is to approximate the probability of an excursion in demand using Chernoff bounds and other large deviation approximations, then chart its recovery to a target acceptable level using the results on transience Interestingly, the time to recover from excursions suf ciently close to the target level depends on the level durations essentially only through their mean.

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Gestation Mating 50% of females sacrificed at day 15 (optional)

5 Fraser, C M A genomics-based approach to biodefence preparedness Nat Rev Genet 2004, 5, 23 33 6 Bronze, M S; Green eld, R A Preventive and therapeutic approaches to viral agents of bioterrorism Drug Discov Today 2003, 8, 740 745 7 Mairuhu, A T A; Brandjes, D P M; van Gorp, E C M Treating viral hemorrhagic fever Idrugs 2003, 6, 1061 1066 8 Kuiken, T; Fouchier, R; Rimmelzwaan, G; Osterhaus, A Emerging viral infections in a rapidly changing world Curr Opin Biotechnol 2003, 14, 641 646 9 Gubler, D J The global emergence/resurgence of arboviral diseases as public health problems Arch Med Res 2002, 33, 330 342 10 Khabbaz, R F Emerging viral infections Adv Pediatr Infect Dis 1999, 14, 1 27 11 Andrei, G; De Clercq, E Molecular approaches for the treatment of hemorrhagic fever virus infections Antiviral Res.

Correspondingly, the conditional mean demand relaxes linearly from its excursion, at least approximately so, for suf ciently small times If the chance for a larger excursion is negligible (as determined by the large deviation approximation mentioned) then this simple description may suf ce An example is given in Section 178 In Section 179 we show how long-range dependence in the level process arises through heavy-tailed level-holding-time distributions Finally, we draw conclusions in Section 1710..

Treatment of the females is continued through pregnancy (21 days) and until the pups are weaned. Pups are usually 21 days of age. The test compound is administered at three dose levels either in the feed, in drinking water, or by gavage. The high dose is chosen to cause some, but not excessive, maternal toxicity (e.g., an approximate 10% decrease in body weight gain, or effects on target organs). Low doses are generally expected to be no-effect levels. After the pre-mating period, the rats are placed in cohabitation, with one male and one female caged together. Mating is con rmed by the appearance of spermatozoa in a daily vaginal smear. Day 1 of gestation is the day insemination is con rmed. The females bear and nurse their pups. After birth, the pups are counted, weighed, and examined for external abnormalities. The litters are frequently culled to a constant number (usually 8 10) after 4 days. At weaning, the pups are killed and autopsied for gross and internal abnormalities. In a multigeneration study, approximately 25/sex/group are saved to produce the next generation. Brother-sister pairings are avoided. Treatment is continuous throughout the test, which can be carried out for two, sometimes, three generations. An abbreviated protocol for a multiple generation test can be seen in Figure 21.3. Note that the parental generation is known as the F0 generation and the

1993, 22, 45 75 12 De Clercq, E Molecular targets for antiviral agents J Pharmacol Exp Ther 2001, 297, 1 10 13 De Clercq, E Antiviral agents: characteristic activity spectrum depending on the molecular target with which they interact Adv Virus Res 1993, 42, 1 55 14 Huggins, J W Prospects for treatment of viral hemorrhagic fevers with ribavirin, a broad-spectrum antiviral drug Rev Infect Dis 1989, 11 (Suppl 4), S750 S761 15 Witkowski, J T; Robins, R K; Sidwell, R W; Simon, L N Design, synthesis, and broad spectrum antiviral activity of 1-beta-D-ribofuranosyl-1,2,4-triazole-3-carboxamide and related nucleosides J Med Chem 1972, 15, 1150 1154 16 Sidwell, R W; Huffman, J H; Khare, G P; Allen, L B; Witkowski, J T; Robins, R K Broad-spectrum antiviral activity of virazole: 1-beta-D-ribofuranosyl-1,2,4-triazole-3carboxamide Science 1972, 177, 705 706 17 Sidwell, R W.

17.4 17.4.1

Mating #1

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