Joseph Fiksel

Dynamic evolution in societal networks

A societal network is defined to be a finite directed graph in which individuals are represented by nodes, and relations between individuals by labelled arcs. Each individual undergoes state transitions at discrete instants of time, so that the societal network may be thought of as a deterministic dynamic process. It is shown that the individuals of such a network may be divided into equivalance classes, so that the original network may be represented by a reduced network containing one node for each equivalence class. Similar results are obtained for a more general type of partition called a “class structure.” The application of these concepts is illustrated in the context of “balanced” networks, which have either positive or negative relations between nodes. The long‐run behavior of societal networks is then examined, and it is shown that any network will eventually reach either a stable state or a periodic pattern of state transitions. In the case of a probabilistic transition rule, it is proved that t...

Quantitative risk analysis for toxic chemicals in the environment

Abstract An overview and basic framework is presented for quantification of human health risks associated with toxic chemicals in the environment. The presentation is designed for program managers who require an introduction to the principles of risk analysis and an understanding of the current state-of-the-art. The basic terminology is explained, the methodological components are reviewed, and a series of procedures is discussed for estimating ambient concentrations, effect potency, and human exposure and risk levels for a chemical substance. Practical considerations are discussed, including the uncertainties introduced by data gaps and modelling assumptions. Finally, a simple numerical illustration of the calculation procedures is presented.