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Lower Bound Comparison

The following theorem, due to J. Hertz, [4], specifies a lower bound on the amount of data needed to specify a network:
 \begin{theorem} A lower bound on the number of gene expression profiles which ... ...imum in-degree k is, for N $>>$\space k: $k log_2(\frac{N}{k})$ \end{theorem}
It is therefore interesting to characterize the behavior of predictor-chooser strategy in relation to lower bound. For this purpose 50 networks for each of several values of N with k=2 were generated. The wild-type perturbation and all single ones were simulated on each network. The chooser was used iteratively in conjunction with the predictor to refine the network hypotheses. The results, shown in figure 14.21, do indeed indicate logarithmic behavior.
  
Figure 14.21: Average number of perturbations vs. network size
\scalebox{0.75}{\includegraphics {lec14_fig/image150_gif.ps}}


Peer Itsik
2001-03-04