Say I want to execute some code at just after a machine receives an entity, but before any internal machine processing has taken place? Similarly, how would I run some code after the machine has completed and just before hand-off to another object?

Is there a quick function rundown or diagram that easily shows what happens (and at what times) within each machine so I know where best to attach custom code to operate on entities passing through the system?

Here's a high level of how I'd see it working: