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Abstract
<p class="first" id="P1">One important feature of the mammalian immune system is the
highly specific binding
of antigens to antibodies. Antibodies generated in response to one infection may also
provide some level of cross immunity to other infections. One model to describe this
cross immunity is the notion of antigenic space, which assigns each antibody and each
virus a point in ℝ
<i>
<sup>n</sup>
</i>. Past studies using hemagglutination data have suggested the dimensionality of
antigenic
space,
<i>n</i>, is low. We propose that influenza evolution may be modeled as a Gaussian
random
walk. We then show that hemagluttination data would be consistent with a walk in very
high dimensions. The discrepancy between our result and prior studies is due to the
fact that random walks can appear low dimensional according to a variety of analyses
including principal component analysis (PCA) and multidimensional scaling (MDS). A
high dimensionality of antigenic space is of importance to modelers, as it suggests
a smaller role for pre-existing immunity within the host population.
</p>