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1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Actual position
Fig. 11.4. Experiment 2. Predicted versus real neuronal layout of C. elegans, setup detailed in
text. Colors correspond to the dierent ganglia shown in Fig. 11.2.
matrix by a uniform repulsive force.
b
We will reproduce this null hypothesis in
Experiment 6. The authors nd an error in this case of E = 26:1% far bigger than
the optimization result, supporting then the optimization process as a meaning-
ful description of the relationship between neuronal arrangement and connectivity
in the worm.
11.4.2. Experiment 2
We noticed that the results presented in [3] can be quantitatively improved by a
separate normalization of the neuron-neuron interaction, and the neuron-muscle
interaction. Given that the adjacency matrix A, and M are distinguishable, it
makes sense to compute the normalization
A
=
A
, and
M
=
M
. In doing
this slight change in the parameters, the error reduces to E = 8:75% which is
noticeable in this scenario (nearly a 10% relative improvement with respect to the
result in Experiment 1). However, qualitatively the results do not seem to change,
see Fig. 11.4.
b
This last prescription seems to us unnecessary because the relatedness matrix even with the zero
values for non existent connections is non singular.
