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Actual position
Fig. 11.3. Experiment 1. Predicted versus real neuronal layout of C. elegans, setup detailed in
text. Colors correspond to the dierent ganglia shown in Fig. 11.2.
11.4.1. Experiment 1
First, we reproduce the results presented in [3] for the dedicated-wire model. In this
case, the matrices A, S and M correspond to the weighted connectivity matrices of
the real data. The parameters
A
, and
M
are set to normalize the neuron-neuron,
and neuron-muscle interaction by the average number of synapses per neurite, 29.44
(or equivalently 58.88 synapses per neuron divided by two neurites per neuron). In
the referenced work
S
is set to 1, with no apparent reason, so we did it. The
results are depicted in Fig. 11.3, dierent colors corresponds to the dierent ganglia
shown in Fig. 11.2. The error E in this approximation is 9:69%.
a
The authors
contrasted this result with the positioning of neurons uniformly at random along
the body of the worm, which raises an E34%, moreover they computed that
the probability of obtaining by chance the results of the optimization is of order
10
68
. They also compare the optimization results against the null hypothesis that
more related neurons are positioned closer to each other. To this end they use
instead of A the \relatedness" matrix, which is a matrix connecting neurons by
number of jumps in the lineage tree, substituting non existent connections in this
a
In the original paper the authors nd an error of 9:71%, we attribute this dierence to the use
of dierent data, since we are using the last update of the data in [7].
