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Because in general E log T log E , this condition is not exactly satis ed, however We therefore introduce small corrective deterministic factors g j , discussed below, and rede ne the yj as yj log mj g j , so that Eyj aj a by de nition Any kind of linear regression of yj on j constitutes an unbiased estimator of a, as the lack of bias does not require decorrelation between the yj , nor knowledge of their variances or distributions A weighted regression where the weights are related to the variances s2 of the yj is preferable, however, as this is the minimum variance j unbiased estimator (MVUE) for the regression problem [48] Intuitively this re nement is signi cant as we know that the s2 are far from equal.

To exploit the j optimality, however, the correlation factors g j and the variances s2 must be j calculated a dif cult task They can nonetheless be well approximated, provided simplifying idealized properties are adopted The particular idealizations chosen here are the following: ID1a: For each xed j the dX j; are stationary sequences of uncorrelated variables IDIb: The processes dX j; and dX jH ; , j T jH , are uncorrelated ID2: The process X and, hence, the processes dX j; are Gaussian The above conditions may appear unduly restrictive at rst; however, the underlying effectiveness of the method is based on P1 and P2, ID1 ID2 being added.

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Systemic administration of compounds such as the herbicide paraquat (Figure 18.4), bleomycin (a cancer therapeutic agent), and nitro urantoin (an antibiotic used for urinary tract infections) initiate a progression of degenerative and potentially lethal lesions in the lung by a mechanism known as redox cycling. These compounds are reduced by cytochrome P450 reductase and NADPH, forming a free radical. Although the free radical could potentially react with tissue macromolecules, one molecule of oxygen is reduced to superoxide that can then be converted to other toxic oxygen species. These reactive compounds may cause peroxidation of cellular membranes. The speci c toxicity of paraquat to the lung results from the uptake of this compound by the polyamine transport system in the lung as well as from the high pulmonary oxygen tension. Nitro urantoin, however, is not actively accumulated in the lung, and its tissue speci city probably results from the high pulmonary oxygen tension.

infection57,58 Within cells, amantadine speci cally inhibits viral uncoating by blocking the activity of the proton channel of the in uenza A M2 protein59 In addition to its very small window of clinical ef cacy, amantadine therapy also has serious toxic side effects For example, amantadine affects the nervous system and approximately 10% of people using the drug experience nervousness, depression, anxiety, dif culty concentrating, and lightheadedness60 But most importantly, amantadine is highly speci c to in uenza A virus and is not effective against other in uenza strains, much less different viral families More analogous to the approach described here is Zicam, an over-the-counter preparation consisting of a highly concentrated zinc gel (zincum gluconicum), which interacts with rhinovirus capsid proteins61,62 Crystallographic evidence suggests the surface of rhinovirus-14 contains binding sites for at least 360 Zn2 ions.

mainly to extend the quantitative analysis. Robustness with respect to departures from these idealizations is discussed in detail below. Note that ID1a and ID1b together make ID1, the idealization of complete decorrelation. It is split here to highlight the fact that ID1b, independence between scales, is not needed for the key results. Under ID1a and ID2 it can be shown [75] that g j is a negative, increasing function of nj only, given by g j c nj =2 = ln 2 log2 nj =2 ; 2:20

There are two important defense mechanisms against inhaled particles. The rst of these involves the mucociliary escalator and consists of the trapping of particles in mucus followed by the upward movement of the mucus brought about by the upward beating of cilia on the airway epithelial airway cells. The material is then either swallowed or expectorated. The second mechanism is macrophage mediated. Macrophages engulf particles and either deposit them on the mucociliary escalator or enter the lymphatic system. Toxicants may also be detoxi ed by xenobiotic-metabolizing enzymes such as cytochrome P450 or the avin-containing monooxygenase. It should be borne in mind, however, that these enzymes may also activate toxicants to more reactive, and potentially more toxic, metabolites.

where c z GH z =G z is the so-called Psi function and G z the Gamma function. This function can easily be calculated for all values of nj . Under ID1a and ID2, with g j as above, the variables yj log mj g j are scaled and shifted logarithms of Chi-squared variables, satisfying Eyj ja log2 cf C; Var yj s2 z 2; nj =2 = ln2 2; j 2:21 2:22

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