Emergence and Evolution of Hierarchical Structure in Complex Systems
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It is well known that many complex systems, both in technology and nature, exhibit hierarchical modularity. What is not well understood however is how this hierarchical structure (which is fundamentally a network property) emerges, and how it evolves over time. Further, the norm is that hierarchical systems are designed incrementally over time to provide support for new outputs and potentially to new inputs. This is very different than re-designing a new system "from scratch" after a change in the outputs or inputs. We propose a modeling framework, referred to as Evo-Lexis, that provides insight to some general and fundamental queries about evolving hierarchical systems. Evo-Lexis models the system inputs as symbols ("sources") and the outputs as sequences of those symbols ("targets"). Evo-Lexis computes the optimized adjustment of a given hierarchy when the set of targets changes over time by additions and removals ("incremental design"). Additionally, Evo-Lexis computes the optimized hierarchy that generates a given set of targets from a set of sources in a static (non-evolving) setting ("clean-slate design"). The questions we focus on are: 1. How do some key properties of this hierarchy, e.g. depth of the network, reuse or centrality of each module, complexity (or sequence length) of intermediate modules, etc., depend on the evolutionary process generating the new targets? 2. Under what conditions do the emergent hierarchies exhibit the so called "hourglass effect"? Why are few intermediate modules reused much more than others? 3. Do intermediate modules persist during the evolution of hierarchies? Or are there "punctuated equilibria" where the highly reused modules change significantly? 4. Which are the differences in terms of cost and structure between the incrementally designed and the corresponding clean-slate designed hierarchies?
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