DIMACS Center, CoRE Building, Rutgers University

**Organizers:****David Ozonoff**, Boston University, School of Public Health, dozonoff@bu.edu**Melvin Janowitz**, Rutgers University, melj@dimacs.rutgers.edu**Fred Roberts**, Rutgers University, froberts@dimacs.rutgers.edu

Many practical epidemiological problems involve the comparison of one or more quantities. Most often the quantities are rates or proportions leading to a measure of effect or association, but they may also involve distances, exposure categories, job titles, etc. Often the actual values in question are not important, only whether one value is smaller than or larger than a second, i.e., their order. This working group will study how fundamental order-theoretic concepts of TCS and DM such as semiorders, interval orders, general partial orders, and lattices [Fishburn (1985), Trotter (1992)] can be used to improve the results of epidemiological investigations. We will give epidemiological concepts a careful definition in the language of partial orders and explore the use of visualization of order-theoretic concepts in epidemiologic studies. The latter will involve issues such as how best to visualize a poset through clever presentation of its Hasse diagram - an issue of great interest in the field of TCS known as graph drawing. One application of these ideas arises in the problem of determining cutoffs or boundaries so as to determine exposure categories in epidemiology. This can be modeled by finding n attributes (age, inverse of distance to a pollution source, etc.); for each subject x, finding a number fi(x) representing a measure of the ith attribute; and saying that x has a higher exposure than y if fi(x) > fi(y) for all i. This defines a partial order that is well studied in dimension theory. Finding the

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Roberts, F.S. (1999), "Meaningless statements," in Graham, R.L., Kratochvil, J., Nesetril, J., and Roberts, F.S. (eds.),
Contemporary Trends in Discrete Mathematics, DIMACS Series, **49**,
American Mathematical Society, Providence, RI, 257-274.

Suppes, P., Krantz, D.H., Luce, R.D., and Tversky, A. (1989),
*Foundations of Measurement*, Vol. II, Academic Press, New York.

Trotter, W.T. (1992), *Combinatorics and Partially Ordered Sets: Dimension Theory*,
The Johns Hopkins University Press, Baltimore, MD.

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Document last modified on February 20, 2004.