Machines from Graphs

[jpfairbanks]

I just worked out the Machines from Graphs example on paper and I'm really excited about it. This is going to be the killer app for "functorial data migration in scientific computing". In this slide
we have talked about how every time a computer scientist uses graphs they are actually doing ACT. The implementation of F: Th(Machines) --> Th(LabeledGraphs) and the pullback data migration functor induces a contravariant functor on their models DF: LabeledGraphs --> Machines is a way to formally discuss how a computer scientist "represents a machine by drawing a labeled graph".

I think we are going to see how CS data structures that are oriented and give rise to processes are C-Sets of categories that have functors into Th(Graph) or Th(BipartiteGraph) and nonoriented mathematical objects are C-Sets of categories that have functors into Th(SymGraph). The pullback migration functors induced by these functors between schemas are going to specify the ways of representing the structure as a graph.

For the case of "a dynamical system represented by a graph, we get the following square, which explains how a dynamical system machine can be derived from "a graph with additional data." The top side of the square shows how the interconnection pattern of the machine is derived from the edge set, and the right side of the square shows how the additional data lives on the graph. The left side shows how the dynamics live over the interconnection pattern and the bottom side shows how to derive the dynamics from the vertex labels.

[slibkind]

Yes! I'm excited about this as well. What do you think are next steps for this?

[jpfairbanks]

Not sure! But I think we need to keep an eye out for this pattern.