  For decades, the hemagglutination-inhibition (HI) assay has been used in
epidemiological and basic biological studies of influenza viruses. The
mechanistic basis of the assay results (called titers) is not well understood.
The first part of this document describes a biophysical model of HI that
illuminates the mechanistic basis of and provides the theoretical motivation
for new ways of interpreting titers. The biophysical model is applicable to
other serological assays; this fact is illustrated using the neutralization
assay. The second part of the document describes some new ways of interpreting
titers, which involve, among other methods, singular value decomposition and
probabilistic multidimensional scaling. The third part of the document
discusses biological and mathematical issues related to the determination of
the effective dimensionality of titers, and describes an algorithm for
recovering unavailable titers.
