Are Copying and Innovation Enough?
T. Evans (Theoretical Physics, Imperial College London) and D. Plato (Theoretical Physics, Imperial College London)
Copying and innovation may be the two most important processes behind a vast range of phenomena. As inheritance and mutation, they are the backbone of genetics but these processes are also the key to understanding many other problems. For instance `scale-free' networks may be so prevalent in data sets because they form when purely local copying is occurring, giving the only natural explanation for 'preferential attachment'.
I will focus on a simple model of network rewiring which uses just copying and innovation processes. I will show how one may solve this exactly for any sized network and for all times. For example this can be used to follow the phase transition in a graph in real time. I will also show how this model is closely related to those used in many other areas: statistical physics, cultural transmission, genetics, econophysics and ecology. As a result it can be seen that regardless of the apparent complications some results obtained elsewhere are actually due to existence of just two simple processes - copying and innovation.