Threshold and dose response estimation using the “filter model”

The “filter model” has been developed to explain the biologic effects of radiation and chemicals. We have examined nearly 300 sets of dose response data, of which 50 are presented here. Responses (induced by radiation and chemicals) which have been examined include in vitro survival studies on animal and plant tissues, induction of cellular aberrations and time to tumor or death. Similar data from in vivo studies has also been examined. All of the data appear to fit the model R = a lnD + b(lnD)² + c, where R is the response, a and b are parameters fitted by regression to a particular set of data, and c is the response at zero (or lowest) dose. By writing this model in exponential form, it can be seen that the response R results from multistage filtering (by net amounts a and b) of the initial dose, D. The threshold is obtained from this model as the point, $\text{D}\text{?}{}_{\mathrm{T}}$, at which the second derivative becomes zero. This is given by $\text{D}\text{?}{}_{\mathrm{T}}\text{=}\text{exp}\text{(1 ?}\text{a}\text{2b}\text{)}$ when a and b are oppositelt signed.     

A note on the allocation of investment

It is shown by example that the results obtained by Gruver [11 concerning specialization of investment in either directly productive or pollution control capital arise because of an implicit linearity assumption on the underlying technology. Utilizing a strictly concave “eighth sphere” technology, results are obtained which imply joint investment in the two types of capital except in “rare” instances. The results indicate the need for incorporating more general technologies into the analysis of such problems.     

A note on natural production functions

Two techniques are presented for estimation of natural animal populations, both of which may incorporate the effect of pollutants on populations. Both techniques assume specific underlying population dynamics which may not be applicable to certain species or ecosystems. However, both techniques allow for testing the hypothesis that the population dynamics specified is applicable. The techniques are used to criticize two recent empirical investigations of fisheries.     

Intertemporal and intergenerational pareto efficiency: A comment

In a recent issue of this Journal, Sandler and Smith developed an analysis from which they concluded that discounting is Pareto inefficient in an intertemporal context. This comment questions the validity of that conclusion and demonstrates the essential role played by the discount rate in achieving intertemporal Pareto efficiency within a market economy.     

The 1934 floods in Tabriz, N. W. Iran

The disastrous floods of July 1934 in Tabriz are examined in the context of the history of floodinginthe city, which is crossed by a dry stream bed liable to sudden Inundation by mountain torrents from the southeast. Few details of past events have survived, suggesting that relatively little significance has been attached to them. Typically, flood dykes were inadequately maintained. This neglect, combined with a radical alteration in urban topography after 1925, when broad straight avenues were constructed through the old heart of the city, led to serious losses from flooding twice in 1929 and again in 1934. Enhanced perception of the flood risk finally found expression in the adoption of large scale engineering measures to mitigate future events, including strengthening protective dykes and widening the river channel through the city. These works have reduced vulnerability to flooding from river overflow. No long-term detrimental Impact of the 1934 flood has been observed. Some of the physical and social parameters that have influenced the vulnerability of Tabrizinthe past continue to be present both there and elsewhere in Iran, and they may be characteristic also of other regions with comparable natural environments or in a similar stage of socio-economic development.