Adaptive rewiring in nonuniform coupled oscillators

Abstract

Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, that is, networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information-processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether nonuniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.

Keywords: Complexity; Dynamical systems; Evolving neural networks; Neural oscillators.

Figure 1.

Network structures of representative models. Each panel shows the unserialized (top left) and serialized (top right) adjacency matrices, and the graph representation (bottom) of the structural connectivity at the last rewiring step. The within-minority, within-majority, and interpartition edges are colored blue, red, and green, respectively. In the graph representation, the minority and majority nodes are colored sky blue and pink, respectively.

Figure 2.

Evolution of network statistics in the baseline (BL) condition for the whole network and majority and minority subgraphs.

Figure 3.

Evolution of network statistics in the less chaotic (LC) condition for the whole network and majority and minority subgraphs.

Figure 4.

Evolution of network statistics in the more chaotic (MC) condition for the whole network and majority and minority subgraphs.

Figure 5.

Evolution of network statistics in the sub-coupled (SC) condition for the whole network and majority and minority subgraphs.

Figure 6.

Evolution of network statistics in the hyper-coupled (HC) condition for the whole network and majority and minority subgraphs.

Figure 7.

Normalized rich-club coefficients of the whole network after the last rewiring step, grouped by condition. Solid circles mark significant values.

Figure 8.

Network structures of terminated models. Panels and color coding are similar to those of Figure 1.

Figure 9.

Heat maps of pairwise dissimilarities of anatomical (top) and functional (bottom) networks. The upper diagonal elements show normalized dissimilarity measures derived from NetSirnile algorithm, and the lower diagonal elements show HHG p values. Model names and family assignments are indicated. Lower dissimilarity (hence higher similarity) measures are coded by brighter colors.

Figure 10.

Heat maps of within- and between-family contrasts for anatomical (top) and functional (bottom) connectivities. The values within cells show the average HHG p values of corresponding family-wise comparisons. Lower contrast measures are coded by brighter colors.

Figure 11.

Between-family differentiation scores of the anatomical and functional networks. Values above 1 (dashed line) imply above-average within-family resemblance compared with other families.

Figure 12.

Graph representation of family resemblance and differentiation in anatomical (top) and functional (bottom) connectivities of the fully evolved models. Edge color and size code between-family contrast and node color captures within-family contrast. Node size is proportional to the differentiation score of the corresponding family. The families with ditferentiation scores above 1 are marked with asterisks.