Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations

Human brain anatomy and function display a combination of modular and hierarchical organization, suggesting the importance of both cohesive structures and variable resolutions in the facilitation of healthy cognitive processes. However, tools to simultaneously probe these features of brain architecture require further development. We propose and apply a set of methods to extract cohesive structures in network representations of brain connectivity using multi-resolution techniques. We employ a combination of soft thresholding, windowed thresholding, and resolution in community detection, that enable us to identify and isolate structures associated with different weights. One such mesoscale structure is bipartivity, which quantifies the extent to which the brain is divided into two partitions with high connectivity between partitions and low connectivity within partitions. A second, complementary mesoscale structure is modularity, which quantifies the extent to which the brain is divided into multiple communities with strong connectivity within each community and weak connectivity between communities. Our methods lead to multi-resolution curves of these network diagnostics over a range of spatial, geometric, and structural scales. For statistical comparison, we contrast our results with those obtained for several benchmark null models. Our work demonstrates that multi-resolution diagnostic curves capture complex organizational profiles in weighted graphs. We apply these methods to the identification of resolution-specific characteristics of healthy weighted graph architecture and altered connectivity profiles in psychiatric disease.Comment: Comments welcom

Network constraints on learnability of probabilistic motor sequences

Human learners are adept at grasping the complex relationships underlying incoming sequential input. In the present work, we formalize complex relationships as graph structures derived from temporal associations in motor sequences. Next, we explore the extent to which learners are sensitive to key variations in the topological properties inherent to those graph structures. Participants performed a probabilistic motor sequence task in which the order of button presses was determined by the traversal of graphs with modular, lattice-like, or random organization. Graph nodes each represented a unique button press and edges represented a transition between button presses. Results indicate that learning, indexed here by participants' response times, was strongly mediated by the graph's meso-scale organization, with modular graphs being associated with shorter response times than random and lattice graphs. Moreover, variations in a node's number of connections (degree) and a node's role in mediating long-distance communication (betweenness centrality) impacted graph learning, even after accounting for level of practice on that node. These results demonstrate that the graph architecture underlying temporal sequences of stimuli fundamentally constrains learning, and moreover that tools from network science provide a valuable framework for assessing how learners encode complex, temporally structured information.Comment: 29 pages, 4 figure

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material

Robust Detection of Dynamic Community Structure in Networks

We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (`optimization variance') and over randomizations of network structure (`randomization variance'). Because the modularity quality function typically has a large number of nearly-degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.Comment: 18 pages, 11 figure

Network Approaches to Understand Individual Differences in Brain Connectivity: Opportunities for Personality Neuroscience

Over the past decade, advances in the interdisciplinary field of network science have provided a framework for understanding the intrinsic structure and function of human brain networks. A particularly fruitful area of this work has focused on patterns of functional connectivity derived from noninvasive neuroimaging techniques such as functional magnetic resonance imaging (fMRI). An important subset of these efforts has bridged the computational approaches of network science with the rich empirical data and biological hypotheses of neuroscience, and this research has begun to identify features of brain networks that explain individual differences in social, emotional, and cognitive functioning. The most common approach estimates connections assuming a single configuration of edges that is stable across the experimental session. In the literature, this is referred to as a static network approach, and researchers measure static brain networks while a subject is either at rest or performing a cognitively demanding task. Research on social and emotional functioning has primarily focused on linking static brain networks with individual differences, but recent advances have extended this work to examine temporal fluctuations in dynamic brain networks. Mounting evidence suggests that both the strength and flexibility of time-evolving brain networks influence individual differences in executive function, attention, working memory, and learning. In this review, we first examine the current evidence for brain networks involved in cognitive functioning. Then we review some preliminary evidence linking static network properties to individual differences in social and emotional functioning. We then discuss the applicability of emerging dynamic network methods for examining individual differences in social and emotional functioning. We close with an outline of important frontiers at the intersection between network science and neuroscience that will enhance our understanding of the neurobiological underpinnings of social behavior