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reduced to E = 8:33%, see Fig. 11.6. Now the results are more striking because
they point out not only that the normalization factor notably aects the results, but
also that the consideration of the weights (number of synapses) between neurons
makes no real dierence in the outcome of the optimization process.
11.4.5. Experiment 5
Equivalently to Experiment 3, we introduce the normalization of the neuron-sensor
connections
S
=
S
in the set up exposed in Experiment 4, i.e. unweighted con-
nectivity matrix. Again the results of the optimization process are worst, with
an error E = 9:62%, see Fig. 11.7. Denitely the inclusion of the normalization
of the neuron-sensor connections provide worst results in terms of global error.
The main reason is that the normalization of neuron-sensor connections enhances
even more the connectivity towards the anterior part of the animal. However,
we think that its elimination is not mathematically consistent, and then it must
be preserved in the same way we preserve the normalization of the other type of
connections.
11.4.6. Experiment 6
At the light of the previous results, we think that the contribution of the actual
neuronal connectivity in the global error of the optimization process is very low.
Following the idea in [3], we used the relatedness of neurons, which is a measure of
distance in the lineage tree (not linearly correlated with the connectivity), instead
of the adjacency matrix. The authors in [3] did something similar and provided
an error signicantly larger than the error considering the actual connectivity. We
simply substituted the adjacency matrix by the relatedness matrix, and normalized
according to the previous Eq. (11.8). The error in this case is E = 11:76%, slightly
larger than the error in Experiment 1 but absolutely comparable, moreover the
scatter of the neuron positions is qualitatively equivalent to that in Experiments 1
to 5, see Fig. 11.8.
11.4.7. Experiment 7
Finally, we want to show the results of a really out-minded experiment where the
true adjacency matrix is replaced by an all-to-all connectivity between neurons.
The result obtained in this particular case, raises an error E = 11:60% which is
comparable to the results so far obtained using the true connectivity matrix, see
Fig. 11.9. This experiment raises serious doubts about the validity of the optimiza-
tion procedure proposed so far, as a way to test the wiring economy principle in
neural networks.
