Predicted Frequency Distribution Research Articles

Modeling distributions of air pollutant concentrations—III. The hybrid deterministic-statistical distribution approach

A general modeling approach is proposed to predict the distribution of air pollutant concentrations and in particular the upper percentiles. The approach is hybrid in that it combines features of both deterministic and statistical distribution models. These features include causality and the attempted quantification of stochastic variability and uncertainty. The properties of deterministic and statistical distribution models are discussed separately and this clarifies the contribution that can be made by hybrid modeling. In this way the underlying assumptions are clearly presented. The range of successful applications of the hybrid approach is briefly reviewed. These involve relatively inert pollutants from urban/industrial, point source, elevated point source and roadway emissions. Areas of further research are outlined which would enhance the routine use of the approach and extend its application. Sufficient development has been undertaken, however, that the present standard set of air pollutant dispersion models could be easily updated to provide hybrid models capable of predicting frequency distributions of air pollutant levels under stipulated assumptions.

Devising an Association Index for Evaluating the Predicted Frequency Distribution by Fararo=Kosaka Model

Devising an Association Index for Evaluating the Predicted Frequency Distribution by Fararo=Kosaka Model

Microsphere passage through intestinal circulation: via shunts or capillaries?

Significant quantities of 9-micron microspheres (20-30%) are not trapped in the intestine following intracardiac or intra-arterial injection, but reach venous blood. Some investigators propose that the passage of 9-micron spheres measures blood flow through noncapillary connections. Because frequency distributions of intestinal capillary diameters and 9-micron spheres overlap, microspheres could simply pass through capillaries. Therefore, we developed simple probabilistic models to predict both the size distribution and the percentage of injected spheres [9 +/- 1 (SD) micron] that should appear in venous blood. Chief assumptions in models are that microsphere delivery and sphere diameter are independent and that microspheres pass through capillaries of equal or larger size. The passage predicted by the models was consistent with values in canine intestinal circulation, demonstrating that passage through capillaries [7.38 +/- 1.4 (SD) micron] adequately accounts for spheres in venous blood. Because the diameters of nominal 9-micron spheres were distributed too narrowly to show a marked sieving effect on passage through the intestinal circulation, we also injected microspheres varying from 5 to 20 micron in diameter. This mixture demonstrated a marked sieving effect. The predicted frequency distribution for microsphere diameters in venous blood agreed with the observed distribution. Our models demonstrate that the passage of 9-micron spheres through capillaries, rather than through "shunts," adequately accounts for the appearance of spheres in venous blood and suggests that the frequency distribution of venous microspheres can provide an in vivo method for estimating the frequency distribution of intestinal capillary diameters.

A micelle model for the sedimentation behavior of bovine beta-casein.

The monomer-single polymer model of G.A. Gilbert (Disc. Faraday Soc. 20 (1955) 68) for moving boundary sedimentation has been used by Payens and colleagues to explain the observed results for bovine caseins, and by Harrington and colleagues to explain the observed results for myosin fibrils. Electron microscope pictures of Buchheim and Schmidt have subsequently revealed micellar beta-casein in the form of slightly elongated or spherical particles having a bimodal size distribution, but with a broad range of particle sizes, at concentrations not too far above the critical micelle concentration. The equilibrium properties of a broadly distributed micellar system can be fitted by the shell model developed by one of us, and in the present article, the shell model is extended to predict the moving boundary sedimentation behavior of such a system. The observed sedimentation patterns, as well as the critical concentration predictions of the monomer-single polymer Gilbert sedimentation model, are satisfactorily described with the present model, based on a continuous distribution of intermediates between monomers and the largest possible spherical micelles. For one example considered, the predicted frequency distribution of molecular weight is in qualitative agreement with the frequency distribution of particle volume found by Buchheim and Schmidt.

Predicting frequency distributions for ozone, NO 2 and TSP from restricted data sets

The results of Ott and Mage (1981) for CO indicate that random sampling yields accurate estimates of the mean and standard deviation. This paper examines the estimates for a cumulative frequency distribution using four different types of data set: (1) continuous monitoring throughout the year, (2) continuous monitoring one week out of every four, (3) random sampling at any time and (4) random sampling only on weekdays between 9.00 a.m. and 5.00 p.m. Data sets for O 3, NO 2 and TSP are used. The results show that random sampling should only be used when there is no restriction on the time of sampling and that option (2) yields very good results indicating a cost-effective way of recording results.