A framework for the construction of generative models for mesoscale structure in multilayer networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks

Alterations in White Matter Microstructure and Connectivity in Young Adults with Alcohol Use Disorder.

Background: Magnetic resonance imaging (MRI) studies have shown differences in volume and structure in the brains of individuals with alcohol use disorder (AUD). Most research has focused on neuropathological effects of alcohol that appear after years of chronic alcohol misuse. However, few studies have investigated white matter (WM) microstructure and diffusion MRI-based (DWI) connectivity during early stages of AUD. Therefore, the goal of this work was to investigate WM integrity and structural connectivity in emerging adulthood AUD subjects using both conventional DWI metrics and a novel connectomics approach. Methods: Twenty-two AUD and eighteen controls (CON) underwent anatomical and diffusion MRI. Outcome measures were scalar diffusion metrics and structural network connectomes. Tract Based Spatial Statistics was used to investigate group differences in diffusion measures. Structural connectomes were used as input into a community structure procedure to obtain a co-classification index matrix (an indicator of community association strength) for each subject. Differences in co-classification and structural connectivity (indexed by streamline density) were assessed via the Network Based Statistics Toolbox. Results: AUD had higher FA values throughout the major WM tracts, but also had lower FA values in WM tracts in the cerebellum and right insula ($p_{\textrm{TFCE}}$ < 0.05). Mean diffusivity was generally lower in the AUD group ($p_{\textrm{TFCE}}$ < 0.05). AUD had lower co-classification of nodes between ventral attention and default mode networks, and higher co-classification between nodes of visual, default mode, and somatomotor networks. Additionally, AUD had higher fiber density between an adjacent pair of nodes within the default mode network. Conclusion: Our results indicate that emerging adulthood AUD subjects may have differential patterns of FA and distinct differences in structural connectomes compared to CON. These data suggest that such alterations in microstructure and structural connectivity may uniquely characterize early stages of AUD and/or a predisposition for development of AU