Abstract
The presence of modular organization is a common property of a wide range of complex systems, from cellular or brain networks to technological graphs. Modularity allows some degree of segregation between different parts of the network and has been suggested to be a prerequisite for the evolvability of biological systems. In technology, modularity defines a clear division of tasks and it is an explicit design target. However, many natural and artificial systems experience a breakdown in their modular pattern of connections, which has been associated with failures in hub nodes or the activation of global stress responses. In spite of its importance, no general theory of the breakdown of modularity and its implications has been advanced yet. Here we propose a new, simple model of network landscape where it is possible to exhaustively characterize the breakdown of modularity in a well-defined way. Specifically, by considering the space of minimal Boolean feed-forward networks implementing the 256 Boolean functions with 3 inputs, we were able to relate functional characteristics with the breakdown of modularity. We found that evolution cannot reach maximally modular networks under the presence of functional and cost constraints, implying the breakdown of modularity is an adaptive feature.
Highlights
Complex networks pervade the evolution and organization of a wide range of systems, from cellular or brain webs to technological graphs
We focus on a subset of the function space fμ : 3 → involving all the feed-forward Boolean network (FFBN) that compute singleoutput Boolean functions fμ : {0, 1}ν → {0, 1} with ν = 3 input variables and one output
We have suggested that the breakdown of modularity (BM) is related to the small-world behavior of complex networks (Valverde and Solé, 2007)
Summary
Complex networks pervade the evolution and organization of a wide range of systems, from cellular or brain webs to technological graphs. Breakdown of Modularity in pushing forward a new approach to brain disease where both brain areas and their connectivity patterns become integrated in a single picture Under this view, neurological disorders including Alzheimer’s disease or schizophrenia to challenged healthy cognition, such as in sleep or awareness, can be understood in terms of faulty intermodule communication (David, 1994; Alexander-Bloch et al, 2010; Meunier et al, 2010; Bashan et al, 2012; Godwin et al, 2015). In order to address these limitations, a simple case study that can be systematically explored would be desirable We propose such a toy model of network landscapes where it is possible to exhaustively characterize BM in a well-defined way. Our analysis suggests that the optimization of specific inputoutput mappings is not always compatible with highly modular structures and how the BM might be an adaptive feature
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