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Current approaches to dynamic community detection in complex networks can fail to identify multi-scale community structure, or to resolve key features of community dynamics. We propose a targeted node removal technique to improve the resolution of community detection. Using synthetic oscillator networks with well-defined "ground truth" communities, we quantify the community detection performance of a common modularity maximization algorithm. We show that the performance of the algorithm on communities of a given size deteriorates when these communities are embedded in multi-scale networks with communities of different sizes, compared to the performance in a single-scale network. We demonstrate that targeted node removal during community detection improves performance on multi-scale networks, particularly when removing the most functionally cohesive nodes. Applying this approach to network neuroscience, we compare dynamic functional brain networks derived from fMRI data taken during both repetitive single-task and varied multi-task experiments. After the removal of regions in visual cortex, the most coherent functional brain area during the tasks, community detection is better able to resolve known functional brain systems into communities. In addition, node removal enables the algorithm to distinguish clear differences in brain network dynamics between these experiments, revealing task-switching behavior that was not identified with the visual regions present in the network. These results indicate that targeted node removal can improve spatial and temporal resolution in community detection, and they demonstrate a promising approach for comparison of network dynamics between neuroscientific data sets with different resolution parameters.

Individual differences in brain functional networks may be related to complex personal identifiers, including health, age, and ability. Dynamic network theory has been used to identify properties of dynamic brain function from fMRI data, but the majority of analyses and findings remain at the level of the group. Here, we apply hypergraph analysis, a method from dynamic network theory, to quantify individual differences in brain functional dynamics. Using a summary metric derived from the hypergraph formalism-hypergraph cardinality-we investigate individual variations in two separate, complementary data sets. The first data set ("multi-task") consists of 77 individuals engaging in four consecutive cognitive tasks. We observe that hypergraph cardinality exhibits variation across individuals while remaining consistent within individuals between tasks; moreover, the analysis of one of the memory tasks revealed a marginally significant correspondence between hypergraph cardinality and age. This finding motivated a similar analysis of the second data set ("age-memory"), in which 95 individuals, aged 18-75, performed a memory task with a similar structure to the multi-task memory task. With the increased age range in the age-memory data set, the correlation between hypergraph cardinality and age correspondence becomes significant. We discuss these results in the context of the well-known finding linking age with network structure, and suggest that hypergraph analysis should serve as a useful tool in furthering our understanding of the dynamic network structure of the brain.

Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in network science to analyze patterns of functional interactions between brain regions. We use dynamic network representations to probe the landscape of brain reconfigurations that accompany task performance both within and between four cognitive states: a task-free resting state, an attention-demanding state, and two memory-demanding states. Using the formalism of hypergraphs, we identify the presence of groups of functional interactions that fluctuate coherently in strength over time both within (task-specific) and across (task-general) brain states. In contrast to prior emphases on the complexity of many dyadic (region-to-region) relationships, these results demonstrate that brain adaptability can be described by common processes that drive the dynamic integration of cognitive systems. Moreover, our results establish the hypergraph as an effective measure for understanding functional brain dynamics, which may also prove useful in examining cross-task, cross-age, and cross-cohort functional change.

We introduce and analyze a within-host dynamical model of the coevolution between rapidly mutating pathogens and the adaptive immune response. Pathogen mutation and a homeostatic constraint on lymphocytes both play a role in allowing the development of chronic infection, rather than quick pathogen clearance. The dynamics of these chronic infections display emergent structure, including branching patterns corresponding to asexual pathogen speciation, which is fundamentally driven by the coevolutionary interaction. Over time, continued branching creates an increasingly fragile immune system, and leads to the eventual catastrophic loss of immune control.