# Rewiring of neurons, seen as actors

This is a continuation of the thread concerning the mix of the Actor Model (AM) with the graphic lambda calculus (GLC) and/or the chemical concrete machine (chemlambda).

A GLC neuron was first defined here, in the freedom sector of the GLC. I shall use the term “neuron”, in a more restrictive sense than previously, as being a GLC actor (example here) which has only one exit half-arrow, possibly continued by a tree of fan-out nodes, which are seen as the axon of the neuron.

I don’t know how to constrain an AM computation with GLC actors so they are all neurons at the preparation stage ad they remain neurons during the computation.

Instead, I wonder if there is any chance to model real neurons this way. That is why I try to obtain a prediction concerning a rewiring pattern.  If this model of computation is pertinent for real neural networks, then we should see this rewiring pattern in the wild.

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Let’s contemplate the following chain of reductions, as seen from the GLC actors point of view. I shall use in fact the chemlambda formalism, but I shall change a bit the notation from the coloured nodes to nodes marked by letters, as in GLC. The fan-in node will be denoted by the letter $\phi$. Recall that the fan-in node  from  chemlambda replaces the dilation node from GLC (actually we reuse the dilation node of GLC and change it into a fan-in node by replacing the emergent algebra moves with the FAN-IN and DIST moves of chemlambda).

The first reduction involves doing an internal DIST move in the actor $a$.

In red, we see the actor diagram, it does not change during this internal interaction.

The next step involves a graphic beta move:

As you see, the actors diagram changed as an effect of the interaction between actors $a$ and $b$.

The next step is a name change interaction between the actors $a$ and $c$, namely $a$ gives a fan-out node to $c$.

That’s it. What is this having to do with neurons?

We may see the fan-out node from the initial configuration, belonging to the actor $a$, as the axon of $a$. Further, we may identify actors $a$ \$ and $d$, and also actors $b$ and $g$. In this way, the whole sequence of three interactions can be rewritten like this:

Notice how I changed the convention of drawing the actors diagram:

• I took care to indicate the orientation of the links between actors
• the fan-out node from the initial configuration was externalized, to look more like an axon, and likewise for the final configuration.

This gives a prediction: if neurons can be modelled as GLC actors, then we should observe in reality the following change of wiring between neurons.

It involves the rewiring of 5 neurons! Are there somewhere in the neuroscience literature patterns of wiring of 5 neurons like the ones from this figure? Is there any evidence concerning a rewiring like in this figure?