Bimodal distribution/variation

It has been found, however, that the acetylation of certain compounds in man and in the rabbit shows wide interindividual variation. This variation in acetylation is a genetic polymorphism in NAT2 and shows a bimodal distribution with two phenotypes, known as rapid and slow acetylators. The slow acetylator has a mutation, which gives rise to a less active form of the enzyme. This is discussed in more detail in the next chapter. 

Major and trace element variations for the Lipari rocks show scattering and a bimodal distribution of compositions (Fig. 7.9). However, detailed studies highlighted distinct trends for several trace elements, especially Zr vs. Sr (see Crisci et al. 1991). Rhyolites display variable abundances for several trace elements such as Zr, Th, and Rb. REE of mafic rocks are fractionated and have flat HREE patterns silicic rocks contain strong negative Eu anomalies (Fig. 7.10a). Incompatible element patterns of mafic rocks are fractionated with negative anomalies of HFSE and positive spikes of Sr and Pb (Fig. 7.10b). 

Variation diagrams of major and trace elements vs. SiC>2 (Fig. 8.13) show a bimodal distribution between basalts and rhyolites, with a gap for intermediate compositions (Daly gap). Such a distribution of rock types is typical of volcanoes from continental rift settings (see Peccerillo et al. 2003 and references therein). A few intermediate samples have been found as xenoliths, and these have been suggested to represent hybrids between mafic and felsic magmas (e.g. Mahood and Baker 1986). 

The first step towards inclusion of a mixture model in a PopPK analysis is often graphical examination of the histograms of the EBEs of the model parameters that are treated as random effects assuming no mixture is present in the distribution of the random effects (i.e., the model does not include a mixture distribution), with clear multimodality used as strong evidence that a mixture distribution should be included in the model. This approach is not ideal since in order to visually detect a bimodal distribution of two normally distributed random variates, the subpopulation means must be separated by at least two standard deviations (Schilling,... 

Figure 8.8 Variation of complex viscosity and storage modulus with frequency, showing the effect of bimodal distribution of stainless steel and alumina in low density polyethylene at 200 C. (Reprinted from Ref. 54.)...

A detailed study on MWD variation during ultrasonic irradiation of different samples of polystyrene (narrow, broad, and bimodal distribution) has been performed by Glynn and van der Hoff. Their results are discussed in Section B of this chapter and Volume 2, Section VIIB.D. Films of narrow-distribution polystyrene have also been milled for several hours at room temperature [50]. As a first step, there is a broadening of MWD with the formation of a bimodal distribution for the case of a medium molecular weight... 

It is seen that the distribution is bimodal, with the coarse mode dominating the aerosol volume concentrations. The 1979 average volume concentration of aerosol less than 10 ym diameter was 32.4 ymVcm. From its large standard deviation, it is clear that the coarse particle mode exhibited considerable variation throughout the year. Records show that high coarse mode volume concentrations accompanied moderate-to-high wind speeds. The coarse material was very likely wind-blown dust of crustal composition. 

Moreover, the size of the polyacrolein blocks depends on the ratio of the propagation rate constant kpr to the transfer rate constant hm (kpr/hm). This ratio may depend on the nature but also on the complexatlon of the living ends. Indeed, an evolution of the complexatlon state exists for the (1,4) living end and may involve a variation of (kpr/hm) (1,4) during the propagation. The previous mechanism can explain the bimodal weight distributions obtained for both homopolyacrolelns and block polymers. 

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