If it's not too much to ask, would you explain some of the other functions and how they relate to the people they were derived from? Ones like Ping confuse me, for example.
When Red absorbs the trace data from them as she finds them, their specific attributes form an attack into the Transistor, as it is, among other things, a weapon. Since it’s built to control and destroy the Process, any program that adapts to it serves as a Function to facilitate those ends.
As to how their data adapts to the Transistor so well is unclear, but it’s probably to do with the fact that they were methodically dispatched by it, creating a connection to them in a way. On approach of each character, as the game goes along, you can also see their “disposition” information pop up. Lillian Platt’s for example, was explosive, matching with Spark().
Not every function is obtained from finding these characters themselves, though, but you can still find clues about their connection on the Function screen. Cull(), for example is described as “Destructive, Kinetic” for Olmarq, a leading player in the Hammers team, who was known to cause a lot of injuries during games. Ping() is described as “Rapid, Efficient” which does make some sense for Henter Jallaford as a prolific, and successful detective.