The spatial distribution of coupling between tau and neurodegeneration in amyloid-ß positive mild cognitive impairment.

Synergies between amyloid-ß (Aß), tau, and neurodegeneration persist along the Alzheimer's disease (AD) continuum. This study aimed to evaluate the extent of spatial coupling between tau and neurodegeneration (atrophy) and its relation to Aß positivity in mild cognitive impairment (MCI). Data from 409 participants were included (95 cognitively normal controls, 158 Aß positive (Aß+) MCI, and 156 Aß negative (Aß-) MCI). Florbetapir PET, Flortaucipir PET, and structural MRI were used as biomarkers for Aß, tau and atrophy, respectively. Individual correlation matrices for tau load and atrophy were used to layer a multilayer network, with separate layers for tau and atrophy. A measure of coupling between corresponding regions of interest (ROIs) in the tau and atrophy layers was computed, as a function of Aß positivity. Fewer than 25% of the ROIs across the brain showed heightened coupling between tau and atrophy in Aß+ , relative to Aß- MCI. Coupling strengths in the right rostral middle frontal and right paracentral gyri, in particular, mediated the association between Aß burden and cognition in this sample.

The spatial distribution of coupling between tau and neurodegeneration in amyloid-ß positive mild cognitive impairment.

Synergies between amyloid-ß (Aß), tau, and neurodegeneration persist along the Alzheimer's disease (AD) continuum. This study aimed to evaluate the extent of spatial coupling between tau and neurodegeneration (atrophy) and its relation to Aß positivity in mild cognitive impairment (MCI). Data from 409 subjects were included (95 cognitively normal controls, 158 Aß positive (Aß+) MCI, and 156 Aß negative (Aß-) MCI) Florbetapir PET, Flortaucipir PET, and structural MRI were used as biomarkers for Aß, tau and atrophy, respectively. Individual correlation matrices for tau load and atrophy were used to layer a multilayer network, with separate layers for tau and atrophy. A measure of coupling between corresponding regions of interest/nodes in the tau and atrophy layers was computed, as a function of Aß positivity. The extent to which tau-atrophy coupling mediated associations between Aß burden and cognitive decline was also evaluated. Heightened coupling between tau and atrophy in Aß+ MCI was found primarily in the entorhinal and hippocampal regions (i.e., in regions corresponding to Braak stages I/II), and to a lesser extent in limbic and neocortical regions (i.e., corresponding to later Braak stages). Coupling strengths in the right middle temporal and inferior temporal gyri mediated the association between Aß burden and cognition in this sample. Higher coupling between tau and atrophy in Aß+ MCI is primarily evident in regions corresponding to early Braak stages and relates to overall cognitive decline. Coupling in neocortical regions is more restricted in MCI.

Demarcating geographic regions using community detection in commuting networks with significant self-loops.

We develop a method to identify statistically significant communities in a weighted network with a high proportion of self-looping weights. We use this method to find overlapping agglomerations of U.S. counties by representing inter-county commuting as a weighted network. We identify three types of communities; non-nodal, nodal and monads, which correspond to different types of regions. The results suggest that traditional regional delineations that rely on ad hoc thresholds do not account for important and pervasive connections that extend far beyond expected metropolitan boundaries or megaregions.

Significance-based community detection in weighted networks.

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical significance. In this paper, we introduce a null for weighted networks called the continuous configuration model. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework involving the null to plant "background" nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods, particularly when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.

Statistical Modeling of the Default Mode Brain Network Reveals a Segregated Highway Structure.

We investigate the functional organization of the Default Mode Network (DMN) - an important subnetwork within the brain associated with a wide range of higher-order cognitive functions. While past work has shown the whole-brain network of functional connectivity follows small-world organizational principles, subnetwork structure is less well understood. Current statistical tools, however, are not suited to quantifying the operating characteristics of functional networks as they often require threshold censoring of information and do not allow for inferential testing of the role that local processes play in determining network structure. Here, we develop the correlation Generalized Exponential Random Graph Model (cGERGM) - a statistical network model that uses local processes to capture the emergent structural properties of correlation networks without loss of information. Examining the DMN with the cGERGM, we show that, rather than demonstrating small-world properties, the DMN appears to be organized according to principles of a segregated highway - suggesting it is optimized for function-specific coordination between brain regions as opposed to information integration across the DMN. We further validate our findings through assessing the power and accuracy of the cGERGM on a testbed of simulated networks representing various commonly observed brain architectures.

Community Extraction in Multilayer Networks with Heterogeneous Community Structure.

Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction directly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We establish consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction on three applications and a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available code is available at https://github.com/jdwilson4/MultilayerExtraction.

Childhood peer network characteristics: genetic influences and links with early mental health trajectories.

BACKGROUND: Peer relationships are important for children's mental health, yet little is known of their etiological underpinnings. Here, we explore the genetic influences on childhood peer network characteristics in three different networks defined by rejection, acceptance, and prosocial behavior. We further examine the impact of early externalizing and internalizing trajectories on these same peer network characteristics. METHODS: Participants were 1,288 children from the Dutch 'Generation R' birth cohort. At age 7, we mapped out children's classroom peer networks for peer rejection, acceptance, and prosocial behavior using mutual peer nominations. In each network, genetic influences were estimated for children's degree centrality, closeness centrality and link reciprocity from DNA using Genome-wide Complex Trait Analysis. Preschool externalizing and internalizing trajectories were computed using parental ratings at ages 1.5, 3, and 5 years. RESULTS: Of the three network properties examined, closeness centrality emerged as significantly heritable across all networks. Preschool externalizing problems predicted unfavorable positions within peer rejection networks and having fewer mutual friendships. In contrast, children with preschool-internalizing problems were not actively rejected by their peers, but were less well-connected within their social support network. CONCLUSIONS: Our finding of significant heritability for closeness centrality should be taken as preliminary evidence that requires replication. Nevertheless, it can orient us to the role of genes in shaping a child's position within peer networks. Additionally, social network perspectives offer rich insights into how early life mental health trajectories impact a child's later functioning within peer networks.

Functional Data Analysis of Tree Data Objects.

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this paper is establishment of a connection between tree data spaces and the well developed area of Functional Data Analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length representation. These representations of trees in Euclidean spaces enable us to exploit the power of FDA to explore statistical properties of tree data objects. A major challenge in the analysis is the sparsity of tree branches in a sample of trees. We overcome this issue by using a tree pruning technique that focuses the analysis on important underlying population structures. This method parallels scale-space analysis in the sense that it reveals statistical properties of tree structured data over a range of scales. The effectiveness of these new approaches is demonstrated by some novel results obtained in the analysis of brain artery trees. The scale space analysis reveals a deeper relationship between structure and age. These methods are the first to find a statistically significant gender difference.