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Description: Adaptive rewiring is the driving force of brain plasticity to form modular, small-world connectivity structure. Highly simplified models for adaptive rewiring represent the dynamic activity of neural masses by coupled logistic maps. Such models have thus far used uniform parametrizations, preventing any cognitive functionality. In order to enable cognitive functions, adaptive rewiring has to be robust to non-uniformity of parameters. Moreover, it should enable function-specific structures to emerge from such parameterization. Coupled logistic maps are characterized by two parameters, namely turbulence (denoted by \alpha), controlling the range of node activation and coupling strength (denoted by \mathcal{E}) between nodes. We study five parameterization conditions of an adaptively rewiring coupled map networks. A baseline (BL) condition with uniform values for \alpha and \mathcal{E} is compared with four conditions in which either \alpha or \mathcal{E} of a subset (viz., minority subgraph) deviates from the remaining units (majority subgraph). These conditions are called: under-turbulent (UT) or over-turbulent (OT), according to \alpha; and under-coupled (UC) or over-coupled (OC), according to \mathcal{E}. For each condition, 10 model instantiations are run for 20 million discrete updates and undergo one million adaptive rewiring steps. To describe the evolution of model network structure, the clustering coefficient, average path length, small-worldness, modularity, degree assortativity, and edge density are calculated, both for the whole network and its minority and majority subgraphs separately. The rich club coefficient is calculated for the final state of the network. Different conditions are compared by representing networks as multivariate distributions of local network statistics. Aggregate scores of within- and between-condition contrast are defined to measure dissimilarity amongst conditions. The degree to which conditions diverge is evaluated statistically. The results show adaptive rewiring to improve all measures substantially (except for average path length), such that highly modular, small-world network structures evolve from random initial conditions, while the structures evolving in different conditions show considerable differentiation. This study offers computational support for robustness of adaptive rewiring algorithm under symmetry-breaking conditions regarding the dynamic evolution of properties characteristic to brain networks. Furthermore, function-specific structures and behaviors emerge from such deviations, implying that functional and structural differentiation can be used to identify functional components in a network, upholding the use of structural and functional connectivity measures in neuroimaging.

License: CC-By Attribution 4.0 International

Has supplemental materials for Adaptive Rewiring on Coupled Logistic Maps with Heterogeneous Parameters on Thesis Commons


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