A persistent problem in health risk analysis where it is known that a disease may occur as a consequence of multiple risk factors with interactions is allocating the total risk of the disease among the individual risk factors. This problem, referred to here as risk apportionment, arises in various venues, including: (i) public health management, (ii) government programs for compensating injured individuals, and (iii) litigation. Two methods have been described in the risk analysis and epidemiology literature for allocating total risk among individual risk factors. One method uses weights to allocate interactions among the individual risk factors. The other method is based on risk accounting axioms and finding an optimal and unique allocation that satisfies the axioms using a procedure borrowed from game theory. Where relative risk or attributable risk is the risk measure, we find that the game-theory-determined allocation is the same as the allocation where risk factor interactions are apportioned to individual risk factors using equal weights. Therefore, the apportionment problem becomes one of selecting a meaningful set of weights for allocating interactions among the individual risk factors. Equal weights and weights proportional to the risks of the individual risk factors are discussed.

Multiple Interacting Risk Factors: On Methods for Allocating Risk Factor Interactions

approved: -^^ "T\ " Richard S. Johnston \ The mathematical theory of information provides a rich basis for the analysis of information systems. Through the definition of communications systems and their parts as probabilistic entities, information theory provides the means to quantify and measure information as a means to uncertainty resolution. Information measured in this context is value-free; the addition of economic theory to information theory offers a means to understanding both the content and the value of information in the fishery. Information acquires value under scarcity conditions of uncertainty. The value of information to the fisherman lies in the increased probability of reaching a desired payoff. The value of pooled information to increased search efficiency is dependent on scale economies. Information networks are a frequently observed phenomenon in open access fisheries characterized by high levels of uncertainty. Although various interpretations have been given to the function an information network serves, the particular focus of this paper is on information as a capital asset in a fishing system. As the fishing system becomes more complex with an increasing number of states, system entropy increases; the value of information as a producer of income also increases. Differences in skill, measured by differential abilities to produce information, result in differences in search costs and income between fishermen. The information produced by each fisherman is a bonus to fishing that, allows the possibility of a network of exchange. An information network in a fishery may be viewed as a production mechanism that reduces transactions costs. In a limited sense, the information network establishes property rights to the fishery by dividing the fishing ground into territories. Uncertainty provides incentives for a market for information. The existence of adaptations that modify the open access condition suggests that the relationship between property rights and use levels may not be causal under conditions of uncertainty. Conditions of uncertainty also raise questions about the appropriateness of standard efficiency evaluations in the fishery. Differential skill in information production emphasizes the contribution of skill to fishing effort. The distinction between real and nominal effort allows a cooperative effect in the application of effort which makes the prediction of fisherman response to a particular policy prescription a complex task. Incentives to adopt various control mechanisms in the fishery ;can be directly related to the type and level of entropy faced by decision makers. An individual fisherman interested in maximizing the return on his investment of effort will resist any restrictions on open scramble competition. A management agency, however, has strong incentives to resist scramble competition. The presence of noise in the transmission process affects the acquisition of information and hence the resolution of uncertainty. The existence of fact or rule uncertainty may have a significant impact on the success of policy implementation. Hypotheses related to the impact of uncertainty on fishermen are generated for testing in the next phase of research. A Theoretical Analysis of Information Networks in the Fishery

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A theoretical analysis of information networks in the fishery

A discrete mathematical extension of conceptual ecological models – Application for the SE Florida shelf

The problem of combining phylogenetic trees (also called evolutionary trees or dendrograms) based on the findings of various experts (or algorithms) in order to select a representative tree that is a consensus of the experts is considered. This research proposes using a genetic algorithm (GA) employing a novel phylogenetic tree code to solve this problem. This encoding scheme insures feasibility after performing the operations of crossover and mutation and also insures the feasibility of the initial randomly generated population (i.e., generation 0).

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Consensus of phylogenetic trees using genetic algorithms

The Human Genome Project (HGP) plans to sequence the human genome by the beginning of the next century. It will generate DNA sequences of more than 10 billion bases and complex marker sequences (maps) of more than 100 million markers. All of these information will be stored in database management systems (DBMSs). However, existing data models do not have the abstraction mechanism for modelling sequences and existing DBMS's do not have operations for complex sequences. This work addresses the problem of sequence modelling in the context of the HGP and the more general problem of an extensible object data model that can incorporate the sequence model as well as existing and future data constructs and operators. First, we proposed a general sequence model that is application and implementation independent. This model is used to capture the sequence information found in the HGP at the conceptual level. In addition, abstract and biological sequence operators are defined for manipulating the modelled sequences. Second, we combined many features of semantic and object oriented data models into an extensible framework, which we called the Extensible Object Model'', to address the need of a modelling framework for incorporating the sequence data model with other types more » of data constructs and operators. This framework is based on the conceptual separation between constructors and constraints. We then used this modelling framework to integrate the constructs for the conceptual sequence model. The Extensible Object Model is also defined with a graphical representation, which is useful as a tool for database designers. Finally, we defined a query language to support this model and implement the query processor to demonstrate the feasibility of the extensible framework and the usefulness of the conceptual sequence model. « less

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Robert M. Thrall

Papers

Discrete Mathematical Models (Fred S. Roberts)