Quantifying heterogeneity

Kell D B, Ryder H M, Kaprelyants A S, Westerhoff H V (1991). Quantifying heterogenity—flow cytometry of bacterial cultures. Anton, van Leeuwen. Int. J. Gen. Mol. Microbiol. 60 145-158. 

Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21 1539-1558,2002. 

Visualizing and Quantifying Heterogeneous Electron Transfer at Electrode Surfaces.668... 

VISUALIZING AND QUANTIFYING HETEROGENEOUS ELECTRON TRANSFER AT ELECTRODE SURFACES... 

Houben [256] has compared the determination of flame-retardant elements Br, P, S, K, Cl and F in polycarbonate using commercial (X40 and UniQuant ) software. For the X40 method, a calibration line for each element in PC or PC/ABS blends was mapped for the conversion of intensities to concentrations. With the universal UniQuant method, sensitivity factors (ks) were calibrated with pure standards. The X40 method turned out to be more reliable than UniQuant for the determination of FRs in PC and PC/ABS blends, even in the case of calibration of k values with PC standards. Standard errors of 5 % were achieved for Br, P, S and K, and 20% for Cl and F the latter element could not be determined by means of UniQuant (Table 8.44). GFR PC cannot be quantified with these two methods, because of the heterogeneous nature of the composites. Other difficult matrices for XRF analysis are PBT, PS and PP compounds containing both BFRs and Sb203 (10-30wt %) due to self-absorption of Sb and interelement effects. 

Different kinds of heterogeneity can be imagined. In the most simple case only a few differing structural entities are found to coexist without correlation inside the volume irradiated by the primary beam. In this case it is the task of the scientist to identify, to separate and to quantify the components of such a multimodal structure. In an extreme case heterogeneity may even result in a fractal structure that can no longer be analyzed by the classical methods of materials science. 

Lobato s work19 makes at least four contributions. First, it seeks to quantify the demand for pharmaceuticals and argues that those variables that are employed in an attempt to approximate physical consumption, such as the number of prescriptions or packages, are not useful because they sum heterogeneous units. Monetary valuation presents the problem (considered below) of what price indexes are to be applied as deflators when studying the evolution of demand and expenditure over time. 

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