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\section{Math}   \hspace{20 mm}Each tumor was modeled as a self-avoiding polygon (SAP). A SAP is a closed shape whose perimeter consists of a random walk path which does not visit the same site more than once, or a self-avoiding walk (SAW). A SAW of length $N$ in the $2$-dimensional lattice &  \input amssym.tex  ${\Bbb R}$  ${\rm \!Z}^d$